23. What lines intersect to form the circumcenter of a triangle?
angle bisectors
midsegments
altitudes
perpendicular bisectors

Answer:

-32x-60y+1122=0

-(32x+60y-1122)=0

32x+60y-1122=0

by factorize

Answer:

24,30

Step-by-step explanation:

Parvati wants to donate enough money to Camosun College

a) Parvati needs to donate $1500 today to fund an annual bursary of $1500

b) The funds must earn a minimum interest rate of 4.75% to sustain an annual bursary

a) To calculate the amount Parvati needs to donate today, we can use the present value formula for an annuity:

PV = PMT / (1 + r)^n

Where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years.

In this case, Parvati wants to fund an ongoing annual bursary of $1,500 with the first payment given out immediately. The interest rate is 4%.

Calculating the present value:

PV = 1500 / (1 + 0.04)^0

PV = $1500

Therefore, Parvati must donate $1500 today to fund the ongoing annual bursary.

b) To determine the minimum amount of interest the funds must earn, we can use the present value formula for an annuity:

PV = PMT / (1 + r)^n

In this case, the donation is $100,000, and the annual payment for the bursary is $4,750 with the first payment given out in one year. We need to find the interest rate, which is represented as j.

Using the formula and rearranging for the interest rate:

j = [(PMT / PV)^(1/n) - 1] * 100

j = [(4750 / 100000)^(1/1) - 1] * 100

j ≈ 4.75%

Therefore, the minimum amount of interest the funds must earn to make the bursary work is 4.75%.

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Answer:

The expression is:

4K

But as an equation, it would be:

T = 4K

Step-by-step explanation:

K = Kelli's age

T = Trey's age

Trey is 4 times older than Kelli

T = (4)(K)

Answer:

Step-by-step explanation:

speed = distance/time

distance= 60m

time= 5 minutes

speed=60m/(5*60 seconds)

speed= .2 m/s

The statement that is true about the graph as it relates the unit rate is:

d. The unit rate is $22.50 per hour

Unit rate of a relationship between two variables, x and y, that are proportionally related can be found using k = y/x, where k is the unit rate.

Given that:

x = hours he worked

y = his total earnings

We are told that (4, 90) is a point on the graph.

Using the point, (4, 90), we can find the unit rate as shown below:

k = y/x = 90/4

k = 22.5

Therefore, the statement that is true about the graph as it relates the unit rate is:

d. The unit rate is $22.50 per hour

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Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.

A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.

By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.

To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.

This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.

Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.

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The value of x is 1.

Since the quadrilateral is a parallelogram, the opposite sides are parallel and have the same length. Therefore, we have:

7 + 3x = yd (1)

y = B4 (2)

3x = 3 (3)

B4 = 3ydB43 (4)

From equation (2), we have y = B4. Substituting this in equation (4), we get:

B4 = 3B43

B43 = B4/3

Substituting this value of B43 in equation (1), we get:

7 + 3x = B4/3

21 + 9x = B4

y = 21 + 9x

Substituting the value of y from equation (2), we get:

B4 = 21 + 9x

3 = 3x

x = 1

Therefore, the value of x is 1.

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Answer: 9 Hours and 30 minutes.

Step-by-step explanation:

on average Ms Johnson takes 15 minutes to mark one English assignment. So to find how long it takes to mark all 38 assignments, mulitply.

15(38)=570 minutes. The problem specifically states to answer in hours. 1 hour is 60 minutes.

570÷60= 9.5.

9 hours and half an hour,

which is 9 hours and 30 minutes.

Answer:

9hours and 30 minutes

Step-by-step explanation:

15x38=570

it takes Ms Johnson 570 minutes

570min=9h 30min

hope this helped

have a great day!!

Answer:

radius= diameter/2= 10/2

*radius=5

circumference= diameter*pi=10*3.14

*circumference=31.4

Step-by-step explanation: hope this helps

Answer:

D

Step-by-step explanation:

1/2 is the same as square root

the square of 8 is 2 root 2

then x squared is 2

and y is 2

16 is to the power of 1/4 is 2

Answer:

Step-by-step explanation:

Because p is a function of hours.

People are a function of hours.

The arc length of the partial circle is, 28.26 units.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Radius of semicircle = 9 units

Now, We know that;

Arc length of semicircle = (2πr) × 180°/360°

Here, Radius of semicircle = 9 units

Hence, We get;

Arc length of semicircle = (2πr) × 180°/360°

Arc length of semicircle = (2 × 3.14 × 9) × 180°/360°

Arc length of semicircle = 28.26 units.

Thus, The arc length of the partial circle is, 28.26 units.

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If the price is $5 before sales tax, it will be $5.5 after sales tax.

A proportional relationship mimics the scenario since the amount spent after sales tax is calculated by multiplying the amount spent before sales tax by a constant.

The following is a generic description of a proportionate relationship:

y = kx.

where k is the proportionality constant.

Since the sales tax rate in this case is 10%, the total amount paid is made up of the following components:

Cost before sales tax.

10% of the cost before sales tax.

The equation is as follows, with x as the price before sales tax:

y = x + 0.1x

simplifying the above equation, we get

y = 1.1x.

Meaning that one point is given as follows:

(5, 5.5).

In other words, if the price is $5 before sales tax, it will be $5.5 after sales tax.

The complete question is:

Dre is painting a mural for his school. Each can of spray paint costs $5 before sales tax. The sales tax rate is 10%. Plot a point that represents how Dre can spend money on spray paint. Cost Including Sales Tax (5)

132

88

44

20

40

60

Cost Before Sales Tax ($)

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Answer:

17.5 hours

I hope this helps and you can give a brainliest!

Step-by-step explanation:

Given: time spent per day follows the arithmetic sequence 1,1.5,2... (for 7 terms) with first term 1 and common difference 0.5 (in hours)

Concept used: the total study time is the partial sum S7of the given arithmetic series.

Calculation: As the number of terms is small, it can be calculated by hand.

S7 = 1+1.5+2+2.5+3+3.5+4

S7= 17.5 hours

Conclusion: Total time spent after one week is 17.5 hours

Answer:

17 and 1/2 hours.

Step-by-step explanation:

this is an arithmetic series  with common difference 0.5 hours.

Number of hours after 7 days

= (n/2)[2a + (n -1)d]

= (7/2)(2*1 + (7-1)0.5)

= 3.5 * 5

= 17.5 hours

It is not differentiable at x=1 since the slope of the tangent line as x -> 1 from the right is 1 while the slope of the tangent line as x->1 from the left is -1

By definition of absolute value:

\(|x - 1| = \begin{cases} x - 1 & \text{if } x \ge 1 \\ -(x-1) & \text{if } x < 1 \end{cases}\)

Then the derivative is

\(\dfrac{d|x-1|}{dx} = \begin{cases} 1 & \text{if } x > 1 \\ -1 & \text{if } x < 1\end{cases}\)

but does not exist at \(x=1\) because

\(\displaystyle \lim_{x\to1^-} f'(x) = -1\)

while

\(\displaystyle \lim_{x\to1^+} f'(x) = 1\)

and these limits are not equal, so the derivative is discontinuous and hence \(|x-1|\) is not differentiable at \(x=1\).

Answer:

the area of triangle

\( \frac{1}{2} \times base \times height \\ → \frac{1}{2} \times 8 \times 7 \\→ 4 \times 7 = 28 {mm}^{2} \)

Step-by-step explanation:

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Answer:

i got you it 10,000

Step-by-step explanation:

all you have to do is add the zeros

The equation representing the minimum and maximum number of fishes which would fit into the tank is : 5 ≤ x ≤ 9

From the table given ;

To represent the maximum and minimum number of fish that will fit into the tank;

We could use an inequality expression to represent these range :

Let x represent the Number of fishes that would fit into the tank :

Therefore, the equation can be written thus :

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The area of the irregular shape is 84 ft square.

The diagram is a trapezium. A trapezium is a quadrilateral. Therefore, the area of the trapezium can be found as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 10 ft

b = 18 ft

c = 6 ft

area of the trapezium = 1 / 2 (10 + 18)6

area of the trapezium = 1 / 2 (28)6

area of the trapezium = 168 / 2

area of the trapezium = 84 ft²

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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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The linear approximation of f at x = π/4 is  1 + 2(x - π/4), the value tan(π/5) is 1 - 3π/40 ≈ 0.3634.

Linear approximation is a technique used in calculus to approximate the value of a function near a particular point using the tangent line of the function at that point. This approximation is often used to simplify calculations and solve problems in a variety of fields, including physics, engineering, and finance.

The linear approximation of a function f(x) near a point a is given by:

L(x) = f(a) + f'(a)(x-a)

where f'(a) is the derivative of the function f(x) evaluated at a. The linear approximation L(x) is the equation of the tangent line to the function at the point (a, f(a)), and it provides an approximation of the function's behavior near that point.

We have,

f(x) = tan x

f'(x) = sec² x

At x = π/4, we have

f(π/4) = tan(π/4) = 1

f'(π/4) = sec²(π/4) = 2

So the linear approximation of f at x = π/4 is given by

L(x) = f(π/4) + f'(π/4)(x - π/4)

 = 1 + 2(x - π/4)

Now, we can use this to estimate tan(π/5) as follows:

tan(π/5) ~ L(π/5)

      = 1 + 2(π/5 - π/4)

      = 1 + 2π/20 - 2π/16

      = 1 + π/40 - π/8

      = 1 - 3π/40

So the estimated value of tan(pi/5) using the linear approximation of f(x) = tan x at x = π/4 is

tan(π/5) ≈ 1 - 3π/40 ≈ 0.3634 (using π ≈ 3.14159).

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The drive-thru is able to estimate their wait time more consistently will be Fast Chicken, because it has a smaller IQR.

In descriptive statistics, the interquartile range tells you the spread of the middle half of the distribution. Quartiles segment any distribution that’s ordered from low to high into four equal parts. The interquartile range (IQR) contains the second and third quartiles, or the middle half of the data set.

The correct option here is Fast Chicken, because it has a smaller IQR (Interquartile Range). IQR is the difference between the third quartile and the first quartile, which is represented by the box in the box plot. In this case, the IQR for Fast Chicken is 14.5 - 10 = 4.5, while the IQR for Super Fast Food is 15.5 - 8.5 = 7. A smaller IQR indicates that the data is more consistent and less spread out.

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The length of the kite and the tail are \(4\frac{2}{3}\) and \(10\frac{5}{6}\) ft respectively.

The tail of the kite is 1.5 feet plus twice the length of the kite.  Together, the kite and tail are 15.5 ft long.  

The length of the tail and the kite can be found as follows:'

let

length of kite = x

Therefore,

length of the tail = 1.5 + 2x

Together the length of kite and tail is 15.5 ft

Hence,

1.5 + 2x + x  = 15.5

1.5 + 3x = 15.5

3x = 15.5 - 1.5

3x = 14

x = 14  /3

x = \(4\frac{2}{3}\) ft

length of the tail =  1.5 + 2(14 / 3)

length of the tail = 1.5 + 28 / 3

length of the tail = 65 / 6 = \(10\frac{5}{6}\) ft

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The score a student would need to have a 30th percentile score on the SAT is approximately 1345. Option B is correct.

To find the score that corresponds to the 30th percentile, we need to use a z-table to determine the z-score that corresponds to a cumulative probability of 0.30.

Using the formula for converting a raw score to a z-score:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and the σ is the standard deviation.

Rearranging this formula to solve for x:

x = z × σ + μ

To find the z-score for a 30th percentile, we can look up the corresponding value in a z-table or use a calculator with a built-in normal distribution function. The z-score corresponding to a cumulative probability of 0.30 is approximately -0.52.

Substituting the known values into the formula above:

x = -0.52 × 312 + 1509

Simplifying:

x ≈ 1345

Hence, B. 1345 is the correct answer.

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Answer: The operation preformed is multiplication.

Step-by-step explanation: When you have a integer that is raised to a power, you must evaluate that integer first. For example, if you are asked to solve 2^3 + 4^7, you must first multiply. 2^3= 8 and 4^7= 16,384 then we must add these two products together to get 16,392.

How to find the product of to the power number: 8^3. We take eight and times it by it's self 3 times to get 512.

Hope this helps!

The correct statements are A, B, and C. If the left-hand limit exists, then the two-sided limit exists (A). If the left and right-hand limits both exist and are equal, then the two-sided limit exists (B). If the two-sided limit exists, then the left- and right-hand limits both exist and are equal (C).

A. If the left-hand limit exists, it means that the function approaches a specific value as x approaches the given point from the left side. In this case, since the left-hand limit exists, it implies that the function is approaching a specific value, which is the same as the two-sided limit.

B. If both the left and right-hand limits exist and are equal, it means that the function approaches the same value from both the left and right sides of the given point. In this case, since the left and right-hand limits are equal, it implies that the two-sided limit exists and is equal to that value.

C. If the two-sided limit exists, it means that the function approaches a specific value as x approaches the given point, regardless of whether it is from the left or right side. In this case, since the two-sided limit exists, it implies that the left and right-hand limits both exist and are equal to that value.

D. This statement is not true. The existence of the right-hand limit alone does not guarantee the existence of the two-sided limit. The left-hand limit also needs to exist and be equal to the right-hand limit for the two-sided limit to exist.

Therefore, statements A, B, and C are true, while statement D is false.

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