Assume the base is 2.

Assume The Base Is 2.

Answers

Answer 1

a = 5

b = 4

c= 0

Therefore, the equation for graph C is Y = a ^b + c

Y = 5 ^4 + 0

What is a graph?

A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Graphs are a popular tool for graphically illuminating data relationships.

A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.

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Related Questions

LA and LB are vertical angles. If mLA=(x+21)° and mLB=(4x-30)°, the find then measure of LB

Answers

Answer:

38 degrees

Step-by-step explanation:

Vertical angles are congruent(equal measures), so mLA = mLB

STEP 1:

Let's use some simple substitution.

mLA = mLB

mLA = x+21, mLB = 4x-30

You plug these two in and get:

x+21 = 4x-30

This is your equation.

STEP 2:

Let's solve our equation!

x+21 = 4x-30

(add 30 to both sides)

x+51 = 4x

(subtract x from both sides)

51 = 3x

(switch order for comprehension)

3x = 51

(divide both sides by 3)

x = 17

Ta-da! You get the measure of x = 17 degrees.

STEP 3:

Let's plug in our value of x to get the value of LB.

mLB = 4x - 30

mLB = 4(17) - 30

mLB = 68 - 30

mLB = 38

This is your answer.

The number of coyotes found in certain state counties is decreasing at a rate of 4. 5% per year. A wildlife biologist recently counted 100 coyotes in one tri-county area. The biologist uses a function to model the population over time and then uses this model to predict the coyote population. Which function model did the biologist correctly use to predict when the population would be fewer than 50 in this tri-county area?

Answers

The biologist predicts that the population would be fewer than 50 in approximately 30 years from the initial count.

The biologist likely used the exponential decay function to model the coyote population over time. This function takes the form:

P(t) = P0 * (1 - r)^t

Where:
P(t) is the population at time t,
P0 is the initial population (100 coyotes),
r is the rate of decrease (0.045 or 4.5%),
t is the time in years.

To predict when the population would be fewer than 50, the biologist would solve the equation:

50 = 100 * (1 - 0.045)^t

t = 30

This equation can be used to find the value of t, which represents the number of years it takes for the population to decrease to fewer than 50 coyotes in the tri-county area, which is 30 years.

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If (arc)mEA=112* and m

Answers

If angle of arc EA is 112 degrees then value of arc IV is 36 degrees by  outside angles theorem

Given that Arc EA measure is One hundred twelve degrees

By Outside Angles Theorem states that the measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs

(112-x)/2=38

112-x=38×2

112-x=76

112-76=x

36 degrees = angle IV or x

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Boris needs to read 2 novels each month.let n be the number of novels boris needs to read in m months.write an equation relating n to m. then use this equation to find the number of novels boris needs to read in 17 months.equation:number of novels in 17 months: i novels

Answers

Solving the equation, Boris needs to read 34 novels in 17 months.

Given that Boris needs to read 2 novels each month.

To relate the number of novels Boris needs to read (n) to the number of months he has to read them (m), we can use the equation:
n = 2m

This equation states that the number of novels (n) is equal to two times the number of months (m) since Boris needs to read 2 novels each month.

Now, to find the number of novels Boris needs to read in 17 months, we can substitute m = 17 into the equation:
n = 2m
n = 2(17)
n = 34

Therefore, Boris needs to read 34 novels in 17 months to meet his goal of reading 2 novels each month.


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solve by completing the square x^2-14x+49=16

Answers

ANSWER:

(x+7)^2=16

Step-by-step explanation:

x^2-14x+49=16

x^2-14x+49-16=0

x^2-14x+33=0

subtract -33 on both sides

x^2-14x+33-33=-33

x^2-14x=-33

Add 49 on both sides

x^2-14x+49=-33+49

x^2-14x+49=16

x^2-7x-7x+49=16

x(x-7)-7(x-7)=16

(x-7)(x-7)=16

(x-7)^2=16

Two straight lines cross at a point.
b+c+d=280°
Work out the sizes of angles a, b, c and d.
a
b
d.
C
Not drawn accurately

Answers

Answer:

a = c = 80°b = d = 100°

Step-by-step explanation:

You want the measures of the angles where lines cross if the sum of three of them is 280°.

Linear pair

Angle b and c form a linear pair, so ...

  b + c = 180°

Substituting that into the given equation, we have ...

  b + c + d = 280°

  180° + d = 280°

  d = 100°

Vertical angles

Angles in this figure that do not share a side are vertical angles, hence congruent.

  b = d = 100°

  c = 180° -b = 180° -100° = 80° . . . . using the linear pair relation

  a = c = 80°

the chance of rain on a random day in May in Gwinnett is about 30%. Using this empirical probability, what would you estimate the probability of having NO rain for an entire week (7 days)?

Answers

The probability of having NO rain for an entire week (7 days) is 0.9998

Estimating the probability of having no rain

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

P(Rain) = 30%

Given that the number of days is

n = 7

The probability of having no rain for an entire week is calculated as

P = 1 - P(Rain)ⁿ

Where

n = 7

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

P = 1 - (30%)⁷

Evaluate

P = 0.9998

Hence, the probability is 0.9998

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Angle BCD is a right triangle. The length of the hypotenuse is 18 centimeters. The length of one of the legs is 13 centimeters. What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box.

Answers

Answer:12.4

Step-by-step explanation:

18^2-13^2=155
Square root of 155 to the nearest tenth is 12.4

Find the radius of an eyebrow window with width 62.8 inches and height 18.5 inches

Answers

The radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches is approximately 36.7 inches.

To find the radius of an eyebrow window, we first need to understand its shape. An eyebrow window is a type of arched window that has a curved shape similar to that of an eyebrow. The shape of an eyebrow window is created by a combination of a circular arc and a straight line.

To find the radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches, we need to use some geometry formulas. The height of the eyebrow window represents the height of the circular arc, and the width represents the diameter of the circle.

The formula for the radius of a circle is r = d/2, where r is the radius and d is the diameter. To find the diameter, we divide the width by pi (3.14). So, the diameter is 62.8/3.14 = 20 inches.

The height of the circular arc is half of the width, which is 18.5/2 = 9.25 inches. To find the radius, we use the formula for the height of a circular arc, h = r(1-cos(a/2)), where h is the height, r is the radius, and a is the angle of the arc.

The angle of the arc can be found using trigonometry. The sine of half the angle is equal to the height divided by the radius. So, sin(a/2) = h/r. Solving for a, we get a = 2arcsin(h/r).

Plugging in the values, we get a = 2arcsin(9.25/r). To find the radius, we solve for r using a calculator or algebra. The radius is approximately 36.7 inches.

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Two days after he bought a speedometer for his bicycle; Lance brought it back (0 the Yellow Jersey Bike Shop. FThele problemn with this speedomeler;' Ba Lance complained to the clerk "Yesterday [ cycled the 22-mile Rogadzo Road Trail in 70 minutes and nOt once did the speedometer read above [5 miles per hour"" Yeah?" responded the clerk " What' $ the problem?" To explain Lance's complaint, first compute his average velocity: (Use decimal notation. Give your answer tO two decimal places ) average velocity: DNE mileshcur Incorrecr

Answers

Therefore, Lance's average velocity was 15.43 miles per hour.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

We can compute Lance's average velocity by dividing the total distance he cycled by the time it took him, and then converting the units to miles per hour.

Total distance: 22 miles

Time: 70 minutes = 70/60 hours

= 7/6 hours

Average velocity = Total distance / Time

= 22 / (7/6)

= 15.43 miles per hour (rounded to two decimal places)

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Estimate the radius of the object. Round to the nearest hundredth if necessary.


C = 8. 9 mm


radius: about


mm

Answers

The estimated radius of the object is about 1.42 mm.

The given information is that the circumference( C) of the object is8.9 mm.

We know that the formula for the circumference of a circle is given by  

C =  2πr  

where r is the compass of the circle.  

To estimate the compass, we can rearrange the formula as

  r =  C/ 2π  

Substituting the given value of C, we get

  r = 8.9/ 2π

we can  estimate this expression to get  

r ≈1.42 mm( rounded to two decimal places)

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Research on the major types of businesses in your province. Based from the data you have gathered, create 1 revenue problem involving quadratic functions. ​

Answers

The top industries are agriculture, mining, tourism, and manufacturing.

The quadratic equations are as given.A manufacturing company in my fiefdom produces and sells ceramic pots.

The company has fixed costs of$ 10,000 per month and variable costs of$ 5 per pot. The company's profit is given by the quadratic function R( x) = -0.2 x2 50x, where x is the number of pots produced and vended in a month.

What's the maximum profit that the company can induce in a month: To break this problem, we can use the formula for chancing the maximum value of a quadratic function, which is given by x = - b/ 2a. In this case, the measure of the x2 term is-0.2, and the measure of the x term is 50. Plugging these values into the formula, we get x = -50/( 2 *(-0.2)) = 125 Hence we obtain the quadratic equation.

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What is the variance of the following set of data?


4, 44, 404, 244, 4, 74, 84, 64

Answers

The variance of the given data set is 18603.39.

To find the variance of the given data set {4, 44, 404, 244, 4, 74, 84, 64}, follow these steps:

Step 1: First, we need to find the mean of the data set:

Mean = (4 + 44 + 404 + 244 + 4 + 74 + 84 + 64) / 8 = 120.5

Step 2: Next, we calculate the deviation of each data point from the mean:

(4 - 120.5) = -116.5

(44 - 120.5) = -76.5

(404 - 120.5) = 283.5

(244 - 120.5) = 123.5

(4 - 120.5) = -116.5

(74 - 120.5) = -46.5

(84 - 120.5) = -36.5

(64 - 120.5) = -56.5

Step 3: Now, we square each deviation:

[tex](-116.5)^2 = 13556.25\\(-76.5)^2 = 5852.25\\(283.5)^2 = 80322.25\\(123.5)^2 = 15252.25\\(-116.5)^2 = 13556.25\\(-46.5)^2 = 2162.25 \\(-36.5)^2 = 1332.25\\(-56.5)^2 = 3192.25[/tex](-116.5)^2 = 13556.25

Step 4: We add up all the squared deviations:

13556.25 + 5852.25 + 80322.25 + 15252.25 + 13556.25 + 2162.25 + 1332.25 + 3192.25 = 130223.75

Step 5: We divide the sum of the squared deviations by the number of data points minus 1 to get the variance:

Variance = 130223.75 / 7 = 18603.39 (rounded to two decimal places)

Therefore, the variance of the data set is 18603.39.

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CD is a perpendicular bisector of chord AB and a chord through CD passes through the center of a circle. Find the diameter of the wheel.



The figure shows a circle. Points A, C, B, E lie on the circle. Chords A B and C E intersect at point D. The length of segment A B is 12 inches. The length of segment C D is 4 inches.




715 in.



10 in.



1425 in.




1215 in.



Need Help ASAP please!!!

Answers

We know that the diameter of the wheel is 1215 inches

Since CD is a perpendicular bisector of AB, it means that CD passes through the center of the circle. Let O be the center of the circle. Then OD is the radius of the circle.

Since chord CE passes through the center O, it is a diameter of the circle. Therefore, CE = 2OD.

Let's use the intersecting chords theorem to find OD.

According to the intersecting chords theorem,

AC * CB = EC * CD

We know that AC = CB (since they are radii of the same circle) and CD = 4 inches. We also know that AB = 12 inches. Let's call the length of segment AE x. Then the length of segment EB is 12 - x.

So we have:

x * (12 - x) = EC * 4

Simplifying:

12x - x^2 = 4EC

Rearranging:

EC = 3x - x^2/4

Now let's use the intersecting chords theorem again, but this time for chords AB and CD:

AC * CB = AD * DB

We know that AC = CB and AB = 12 inches. Let's call the length of segment AD y. Then the length of segment DB is 12 - y.

So we have:

x^2 = y * (12 - y)

Simplifying:

y^2 - 12y + x^2 = 0

Using the quadratic formula:

y = (12 ± sqrt(144 - 4x^2))/2

We can discard the negative solution (since y is the length of a segment, it cannot be negative), so:

y = 6 + sqrt(36 - x^2)

Now let's use the fact that CD is a perpendicular bisector of AB to find x.

Since CD is a perpendicular bisector of AB, it divides AB into two segments of equal length. Therefore,

AD = DB = 6

Using the Pythagorean theorem in triangle ACD:

AC^2 + CD^2 = AD^2

Substituting the values we know:

x^2 + 4^2 = 6^2

Solving for x:

x = sqrt(20)

Now we can find EC:

EC = 3x - x^2/4

Substituting x:

EC = 3sqrt(20) - 5

Finally, we can find OD:

AC * CB = EC * CD

Substituting the values we know:

(2OD)^2 = (3sqrt(20) - 5) * 4

Simplifying:

OD^2 = 12sqrt(20) - 20

OD = sqrt(12sqrt(20) - 20)

We are asked to find the diameter of the circle, which is twice the radius:

Diameter = 2OD = 2sqrt(12sqrt(20) - 20)

This is approximately equal to 1215 inches.

So the answer is:

The diameter of the wheel is 1215 inches.

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Create trig ratios for sin, cos, and tan

Answers

Sin(z) = 4/5, Cos(z) = 3/5, tan(z) = 4/3

We know that

sin(z) = perpendicular/hypotenuse

cos(z) = base/hypotenuse

tan(z) = perpendicular/base

Now putting we get,

Sin(z) = 4/5

Cos(z) = 3/5

tan(z) = 4/3

4


Consider the inequalities -1/4a > 3 a and b – 12> -3. What values, if any, make


both inequalities true? Show your work.

Answers

To solve the inequality -1/4a > 3a, we need to first multiply both sides by -4 to get rid of the fraction:
-1a > 12a
Next, we can subtract 12a from both sides to get:
-13a > 0
Dividing both sides by -13 gives us:
a < 0

To solve the inequality b – 12 > -3, we can add 12 to both sides:
b > 9

Now we need to find values of a and b that satisfy both inequalities. Since a < 0, we can try any negative value of a. Let's try a = -1:

-1/4(-1) > 3(-1)
1/4 > -3

This inequality is true, so we can move on to the next inequality. Let's plug in a = -1 and see if it satisfies b > 9:

b – 12 > -3
b > 9

Since -1 satisfies both inequalities, the values that make both inequalities true are: a = -1 and any value of b greater than 9.

The mean number of sit-ups


done by a group of students is


46 with a standard deviation


of 7. If Rylee's Z-score was


1. 8, how many sit ups did she


do?

Answers

Rylee did approximately 58.6 sit-ups.

We are given that the mean number of sit-ups is 46 and the standard deviation is 7. We are also given that Rylee's Z-score was 1.8, we can use the formula for Z-score to find how many sit-ups she did.

The formula for Z-score is [tex]Z = \frac{X-\mu}{\sigma}[/tex]

Z = Z-score

μ = mean

σ = standard deviation

X = ?

Substituting these values into the formula

1.8 = (X - 46)/7

1.8 × 7 = X - 46

X - 46 = 12.6

X = 12.6 + 46

X = 58.6

Therefore, Rylee did approximately 58.6 sit-ups.

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Question 6 < - Find the linear approximation of f(x) = In x at x = 1 and use it to estimate In(1.16). L(x) = In(1.16) Question Help: Video Message instructor Submit Question Question 5 Use linear ap

Answers

The linear approximation of f(x) = ln(x) at x = 1 is L(x) = x - 1. Using this approximation, we can estimate ln(1.16) to be approximately 0.16.

The formula for the linear approximation of a function f(x) at a point x = a is given by L(x) = f(a) + f'(a)(x - a), where f'(a) is the derivative of f(x) evaluated at x = a.

In this case, f(x) = ln(x), so f'(x) = 1/x by the derivative of natural logarithm.

We are asked to find the linear approximation of f(x) = ln(x) at x = 1, so a = 1 in the formula.

Plugging in the values, we get L(x) = ln(1) + 1( x - 1) = x - 1.

Now, we can use this linear approximation L(x) = x - 1 to estimate ln(1.16) by plugging in x = 1.16, as given in the question.

L(1.16) = 1.16 - 1 = 0.16, which is our estimated value for ln(1.16) using the linear approximation.

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y=1.5 In(et.t+5) for t=1; round your answer to the whole number (exponent "t.t" read (means) t square)

Answers

when t=1, y is approximately equal to 5.

To solve for y when t=1 in the equation y=1.5 In(et.t+5), we first need to plug in t=1:

y=1.5 In(e(1)(1)+5)

We simplify the exponent e(1)(1) to just e:

y=1.5 In(e+5)

Using the properties of natural logarithms, we can simplify this further:

y=1.5(1+ln(5+e))

We can use a calculator to evaluate ln(5+e) to be approximately 2.063, so we can plug that in and simplify:

y=1.5(1+2.063)

y=1.5(3.063)

y=4.5945

Rounding this answer to the nearest whole number, we get:

y=5

Therefore, when t=1, y is approximately equal to 5.

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6 Moses makes a school spirit flag. He has as many yards of red fabric as blue


fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and


blue fabric. Use x to represent the amount of blue fabric. Which equations could


you use to find the amount of red fabric Moses has? Select all that apply.


A X =


B x= x + 2?


x = 2


1/x + 273


x= 1/3x - 223


E x + 2 2 2 = 1/3 x + 2 2 3


C X=


D x- 27 28 = 1/3 x


F * = }}x+ 2


2 2 3

Answers

The equations to find the amount of red fabric Moses has are X = x + 2 and X + 222 = 1/3x + 223. These equations are obtained by using x as the amount of blue fabric and setting up equations based on the given information. So, the correct answer is A) and E).

There are two equations that can be used to find the amount of red fabric Moses has

X = x + 2, This equation represents the fact that Moses bought 2 more yards of red fabric than he originally had of blue fabric. So, the amount of red fabric (X) is equal to the amount of blue fabric (x) plus 2.

X + 222 = 1/3x + 223, This equation represents the fact that after buying 2 more yards of red fabric, Moses has equal amounts of red and blue fabric.

So, the amount of red fabric (X) plus 222 (the additional 2 yards he bought) is equal to one-third of the amount of blue fabric (1/3x) plus 223 (the original 2 yards of red fabric he had).

Therefore, the equations that could be used to find the amount of red fabric Moses has are A) and E).

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--The given question is incomplete, the complete question is given

" 6 Moses makes a school spirit flag. He has as many yards of red fabric as blue fabric. He buys 2 yards more red fabric. Now he has equal amounts of red and blue fabric. Use x to represent the amount of blue fabric. Which equations could you use to find the amount of red fabric Moses has? Select all that apply.

A X = x + 2

B x = 2

C 1/x + 273

D x= 1/3x - 223

E x + 2 2 2 = 1/3 x + 2 2 3

F x- 27 28 = 1/3 x

G = x+ {{22}*2}^3 "--

Issac wants to save up some money to buy a new smartphone, so he babysits on the weekends. There is a proportional relationship between the time Oscar spends babysitting(in hours) , z, and the amount of money he earns babysitting(in dollars) , y. What is the constant of proportionality? Write your answer as a whole number or decimal

Answers

The constant of proportionality represents the rate at which Issac earns money while babysitting and can be found by dividing the amount of money he earns by the time spent babysitting.

Let's say that Issac earns $10 per hour of babysitting. Then, the constant of proportionality would be:

$10 per hour = $10/1 hour = 10

Therefore, the constant of proportionality is 10, which means that Issac earns $10 for every hour of babysitting. This relationship is an example of proportionality because the amount of money earned is directly proportional to the time spent babysitting. As Issac spends more time babysitting, he will earn more money in a proportional relationship.

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roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax what was the total for rogers purchased

Answers

After the discount and the tax, the amount that Roger pays is $45.41

How to find the final price?

We know that Roger purchased a pair of pants for 34.50 and a new a new for 12.00 he had a 10% discount on his total purchased and paid 8.5% sales tax, then the total cost before the discount and tax is:

C = 12.00 + 34.50 = 46.50

Now we apply the discount and the tax (as factors in a product) to get:

C' = 46.50*(1 - 0.1)*(1 + 0.085) = 45.41

That is the amouint that Roger pays for the two items.

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dylan used a styrofoam cone to make a floral arrangement. the cone had a radius of 4.5 inches and a height of 6 inches. what is the volume of this cone? (round your answer to the nearest tenth.)

Answers

The volume of this cone is approximately 127.2 cubic inches

Hi! To calculate the volume of the Styrofoam cone used by Dylan to make a floral arrangement, we can use the formula for the volume of a cone: V = (1/3)πr²h. The cone had a radius of 4.5 inches and a height of 6 inches.

Substituting these values into the formula, we have:
V = (1/3)π(4.5)²(6)

V ≈ 127.2 cubic inches (rounded to the nearest tenth).

So, the volume of this cone is approximately 127.2 cubic inches.

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Name:


Date:


Lesson 02. 05: Module Two Project-Based Assessment


Printable Assessment Module Two Project Based Assessment


Module Two Project-Based Assessment


Part 1


The table shows the measurements of shooting stars that were measured. Use the table


to complete the activities below.


Shooting star length


(in feet)


Number


10


2


8


10


6


8


6


10


7


8


10





4


1. Compare the sizes. Think about the number of Xs that would appear on the line plot.


Write the shooting star lengths in the correct box.


Fewer than 5 Xs


More than 5 Xs


COM


10


2. Complete the line plot for the given set of data.


Lengths of Shooting Stars


7


O


2


Measurement in feet

Answers

5 or more Xs

How to complete the line plot?

To complete the activities based on the given data:

Compare the sizes: By looking at the shooting star lengths, we can determine the number of Xs that would appear on the line plot. The shooting star lengths "10" and "8" appear more than 5 times, so they would be placed in the "More than 5 Xs" box. The shooting star lengths "6" and "4" appear fewer than 5 times, so they would be placed in the "Fewer than 5 Xs" box.

Complete the line plot: Using the given set of data, we can create a line plot to represent the lengths of shooting stars. We mark each measurement on the number line and place an X above the corresponding value.

The line plot would have an X above the number 10, 8, 6, and 4, each representing the occurrence of shooting stars with those lengths.

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Find the measure of angle D.

Answers

The measure of angle D is 25°

What is exterior angle theorem?

Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the opposite interior angles.

Angle D and angle C are the two opposite angles.

Therefore;

40+9x-2 = 20x +5

38+9x = 20x +5

38-5 = 20-9x

11x = 33

divide both sides by 11

x = 33/11

x = 3

Therefore since angle D = 9x-2

substitute 3 for x

D = 9(3) - 2

D = 27 -2

D = 25°

Therefore the measure of angle D is 25°

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what is the value of sin 45 but as a fraction?

Answers

The exact value of sin 45° is [tex]\dfrac{\sqrt{2} }{2}[/tex]

Since we have given that

[tex]\text{sin} \ 45^\circ[/tex]

We need to find the exact value of sin 45°.

From the trigonometric table,

[tex]\text{sin} \ 45^\circ=\dfrac{1}{\sqrt{2}}[/tex]

We need to write it as a simplified fraction,

So, for this, we will rationalize the denominator:

[tex]\dfrac{1}{\sqrt{2}}\times\dfrac{\sqrt{2} }{\sqrt{2}}[/tex]

[tex]=\dfrac{\sqrt{2} }{2}[/tex]

Hence, the exact value of sin 45° is [tex]\dfrac{\sqrt{2} }{2}[/tex]

Answer: 1 divided by the square root of 2

Step-by-step explanation:

Let's set up an example, if the angle is forty five degrees, and the opposite length is 1, we can solve this as sin to get to the hypotenuse,

1. sin(45) = 1/hyp

2. sin(45) times hyp = 1

3. hyp = sin(45)/1

If we take any answer and put it over the hypotenuse as sin, we can see that it is going to end up as 1/√2, or 0.707

I did 1 because you are just asking for sin(45).

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Answer:

CD = 34 units

--------------------------

Since CD is diameter, therefore the angle CAD opposite to it is a right angle.

We are given the lengths of two legs, AD = 16 and AC = 30.

Use Pythagorean theorem to find the length of the hypotenuse CD:

CD² = AD² + AC²CD² = 16² + 30²CD² = 1156CD = √1156CD = 34

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Answers

The line y=10x will in this instance pass through most of the data points, demonstrating that it is a good fit for the data.

A good line of fit should travel across the greatest number of data points and exhibit a positive connection.

What exactly is a scatter plot?

A relationship between two variables in which rising values of one cause rising values of the other. On a scatter plot, it is shown as a positive slope.

The line y=10x will in this instance pass through most of the data points, demonstrating that it is a good fit for the data.

The line will be favourably sloped, so as the duration of an accessible bike rental increases, so does the total cost charged.

The scatterplot confirms this, proving that the line y=10x is a good match for the data.  

This indicates that the data points are nearly aligned with the line but not exactly so.

A good line of fit should travel across the greatest number of data points and exhibit a positive connection.

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prove that the following triangles are congurent

Answers

Answer:

Step-by-step explanation:

Congruent triangles are triangles that are the same shape and same size.

So if they look the same and have the same dimension like area and perimeter then they are congruent.

Mr. Smith invested $2500 in a savings account that earns 3% interest compounded


annually. Find the following:


1. Is this exponential growth or exponential decay?


2. Domain


3. Range


4. Y-intercept


5. Function Rule

Answers

The 99% confidence interval for the population mean is between 39.18 and 62.82, assuming that the population is normally distributed.

How to find the range of the population?

To construct a confidence interval for the population mean, we need to make certain assumptions about the distribution of the sample data and the population. In this case, we assume that the population is normally distributed, the sample size is small (less than 30), and the standard deviation of the population is unknown but can be estimated from the sample data.

Using these assumptions, we can calculate the confidence interval as:

CI = X ± tα/2 * (s/√n)

Where X is the sample mean, tα/2 is the critical value of the t-distribution with degrees of freedom (n-1) and a confidence level of 99%, s is the sample standard deviation, and n is the sample size.

Plugging in the values from the provided data, we get:

CI = 51 ± 2.898 * (17/√18)

CI = (39.18, 62.82)

Therefore, with 99% confidence, we can estimate that the population mean is between 39.18 and 62.82 based on the provided data.

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