A swimming club has three types of members: adults, juniors and children.

The ratio of juniors to children is 1 : 3.

The ratio of children to adults is 5 : 2.

What is the ratio of juniors to adults in its simplest form?

It should be 4 because if you divide everything up it should get you 4 every time

Answer:

y is equal to 0.4x

Step-by-step explanation:

Graph proportational graph

The percentage change in laptop orders is 83%

Percentage is a measure of frequency. It the fraction of an amount expressed as a number out of hundred. Percentages are represented with the sign %.

In order to determine the percentage change, the first step is to determine the change in laptop leased.

Change in laptops leased = 22 - 12 = 10 laptops

This means that the number of laptops leased increased by 10

The second step is to express the change laptops leased  as a fraction of the laptop leased last year and multiply by 100

10/12 x 100 = 83%

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Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

1/9 or 16/18

Step-by-step explanation:

Answer:

Pink, shiny cars were preferred by buyers at that time

Step-by-step explanation:

Rewriting the sentence, removing unnecessary words

Answer:

  h(x) = (x -1)(x +3+√2)(x +3-√2)

Step-by-step explanation:

You want the linear factors of h(x) = x^3 +5x^2 +x -7, given that 1 is a zero.

If 1 is a zero, then (x -1) is a factor. The remaining quadratic factor can be found using synthetic division, as shown in the attachment. This tells us the factorization is ...

  h(x) = (x -1)(x^2 +6x +7)

The factors of the quadratic can be found by completing the square:

  x^2 +6x = -7

  x^2 +6x +9 = 2 . . . . . . . add (6/2)^2 = 9 to both sides

  (x +3)^2 = 2 . . . . . . . . show as a squre

  x +3 = ±√2 . . . . . . . . take the square root

  x +3 ±√2 = 0 . . . . . . subtract ±√2; the two remaining factors

This tells us that h(x) = 0 when (x +3 +√2) = 0 and when (x +3 -√2) = 0. These binomial expressions are the remaining linear factors of h(x).

  h(x) = (x -1)(x +3+√2)(x +3-√2)

The quotient of 3 8 and 2 3 is equal to 4. This can be determined by dividing 3 8 by 2 3 and simplifying the fractions. The result is 4.

To determine the quotient of 3 8 and 2 3, begin by dividing 3 8 by 2 3. This can be done by multiplying the numerator (3) and denominator (8) of 3 8 by the reciprocal of 2 3, which is 3 2. Doing this yields 9 16. Now, reduce the fraction by dividing both the numerator and denominator by the greatest common factor (GCF) of 9 and 16, which is 3. The result is 3 5. Finally, convert the fraction to a whole number by dividing the numerator (3) by the denominator (5). The result is 4. Therefore, the quotient of 3 8 and 2 3 is 4.

3 8 ÷ 2 3 = (3 × 3 2) ÷ (8 × 3 2) = 9 16 ÷ 9 2 = 9 16 ÷ 3 = 3 5 = 3 ÷ 5 = 4

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Answer:

About 5.5% decrease

Step-by-step explanation:

Here, we want to calculate the percentage increase or decrease and its value.

The first thing to do here is to check if we are going to have a decrease or an increase.

since the value before the change is higher than the value after the change, then what we have is a decrease.

Mathematically, the percentage decrease is calculated as follows;

% decrease = (old value - new value)/old value * 100%

old value = 163 feet

new value = 154 feet

% decrease = (154-163)/163 * 100%

% decrease = -9/163 * 100%

% decrease = -5.52%

Thus the best answer is about 5.5% decrease

The function \(B(t) = 182(1.065)^t\) represents the annual population of bees in a county park, the growth rate is 6.5%.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

From the function \(B(t) = 182(1.065)^t\):

b = 1.065

Growth rate = 1.065 - 1 = 0.065 = 6.5%

The function \(B(t) = 182(1.065)^t\) represents the annual population of bees in a county park, the growth rate is 6.5%.

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The corresponding impact and probability of the risk occurring is, low impact and low probability.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

As given: kyle has planned a photo shoot for an outdoor location. the weather forecast predicts a 10% chance of showers in the morning, but sunny skies by lunchtime. the photographer has equipment that can handle rain and light variations.

The variations are there, therefore the corresponding impact and probability of the risk occurring is, low impact and low probability.

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Answer:

a. 20

b. 5

Step-by-step explanation:

The scale factor is 5 because 6×5=30

a. 4×5=20

b. 25÷5=5

Answer:

p and q value is 70 deg and r,s,t and u is 110 deg

Step-by-step explanation:

I. If half circle = 180°

 when p = q = 70°

 so r = s = t = u = 180 - 70 = 110°

Step-by-step explanation:

\(thank \: you\)

By combining the terms with the same units and performing the addition, we simplify the expression (8.2×10^3 s) + (9.7×10^4 s) + (0.006×10^6 s) to 1.517 × 10^4 s.

To simplify the expression (8.2×10^3 s) + (9.7×10^4 s) + (0.006×10^6 s), we can combine the terms with the same units and perform the addition.

First, let's convert all the numbers to scientific notation with the same exponent:

8.2×10^3 s = 8.2×10^3 s

9.7×10^4 s = 0.97×10^5 s

0.006×10^6 s = 6×10^3 s

Now, we can add the numbers:

8.2×10^3 s + 0.97×10^5 s + 6×10^3 s = (8.2 + 0.97 + 6) × 10^3 s = 15.17 × 10^3 s

To express the result in proper scientific notation, we need to normalize the coefficient. In scientific notation, the coefficient should be greater than or equal to 1 and less than 10:

15.17 × 10^3 s = 1.517 × 10 × 10^3 s = 1.517 × 10^4 s

Therefore, the simplified form of the expression (8.2×10^3 s) + (9.7×10^4 s) + (0.006×10^6 s) is 1.517 × 10^4 s.

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Loan repayment: Each semiannual payment is $879.92.

Machine cost: The equivalent uniform annual cost is $6,541.34.

Loan Repayment:

1. Calculate the semiannual interest rate: Divide the annual interest rate (8%) by the number of compounding periods per year (2) to get the semiannual interest rate (4%).

2. Calculate the number of compounding periods: Since the loan is repaid in four equal semiannual payments, there are a total of eight compounding periods (4 years x 2).

3. Calculate the present value factor: Use the formula for the present value of an annuity to calculate the present value factor for eight periods at a semiannual interest rate of 4%.

4. Determine the payment amount: Divide the loan amount ($3000) by the present value factor from step 3 to find the equal semiannual payment.

Machine Cost:

1. Calculate the semiannual interest rate: Divide the annual interest rate (8%) by the number of compounding periods per year (2) to get the semiannual interest rate (4%).

2. Calculate the number of compounding periods: Since the useful life of the machine is 6 years and compounding occurs semiannually, there are a total of 12 compounding periods (6 years x 2).

3. Calculate the future value factor: Use the formula for the future value of a single sum to calculate the future value factor for 12 periods at a semiannual interest rate of 4%.

4. Determine the equivalent uniform annual cost: Subtract the future value of the machine ($9,000) from the initial cost of the machine ($30,000) and divide by the future value factor from step 3 to find the equivalent uniform annual cost.

By following these steps and performing the calculations, you will determine the semiannual payment for the loan and the equivalent uniform annual cost of the machine.

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Answer: 3 and 7

Step-by-step explanation: beucase the color

Answer:

40.8 i think

Step-by-step explanation:

Answer: 40.8

Step-by-step explanation:

Circumference of a circle formula: C=2πr

2⋅6.5⋅π

13π

40.84070450...

40.8

Answer:

17

Step-by-step explanation:

Since we are evaluating g(x) for g(4), we would substitute x in the equation with 4.

x² + 1

(4)²+ 1

16 + 1

17

I hope this helps

The completed table represents the values of the missing entries for the given equation y = x² - 4x + 4.

To determine the values of the missing entries and complete the table, we need to substitute the given values of x into the equation y = x² - 4x + 4 and evaluate the corresponding y-values. Let's start:

For x = 0:

y = (0)² - 4(0) + 4

y = 0 - 0 + 4

y = 4

So, the ordered pair is (0, 4).

For x = 1:

y = (1)² - 4(1) + 4

y = 1 - 4 + 4

y = 1

So, the ordered pair is (1, 1).

For x = 2:

y = (2)² - 4(2) + 4

y = 4 - 8 + 4

y = 0

So, the ordered pair is (2, 0).

For x = 3:

y = (3)² - 4(3) + 4

y = 9 - 12 + 4

y = 1

So, the ordered pair is (3, 1).

For x = 4:

y = (4)² - 4(4) + 4

y = 16 - 16 + 4

y = 4

So, the ordered pair is (4, 4).

Completing the table:

x y

0 4

1 1

2 0

3 1

4 4

Therefore, the completed table represents the values of the missing entries for the given equation y = x² - 4x + 4.

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Answer:

7 pounds.

Step-by-step explanation:

3.60 for 3 pounds

1.20 per pound.

8.40/1.20 = 7 pounds

To verify the identity sin(x) + sin(2x) + sin(3x) = sin(2x)(1 + 2cos(x)), we'll simplify the expression on the left side and compare it to the right side.

Using the identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B), we can rewrite sin(2x) as 2sin(x)cos(x). Similarly, sin(3x) can be expressed as sin(x + 2x) = sin(x)cos(2x) + cos(x)sin(2x).

Now, let's substitute these values back into the left side of the equation:

sin(x) + sin(2x) + sin(3x) = sin(x) + 2sin(x)cos(x) + sin(x)cos(2x) + cos(x)sin(2x).

Rearranging the terms, we get:

sin(x) + sin(2x) + sin(3x) = sin(x) + sin(x)cos(2x) + 2sin(x)cos(x) + cos(x)sin(2x).

Factoring out sin(x), we have:

sin(x) + sin(2x) + sin(3x) = sin(x)(1 + cos(2x)) + 2sin(x)cos(x) + cos(x)sin(2x).

Next, we'll use the double-angle identity \(cos(2x) = 1 - 2sin^2(x)\) to substitute in for cos(2x):

\(sin(x) + sin(2x) + sin(3x) = sin(x)(1 + (1 - 2sin^2(x))) + 2sin(x)cos(x) + cos(x)sin(2x).\)

Simplifying further:

sin(x) + sin(2x) + sin(3x) = sin(x)(2 - 2sin^2(x)) + 2sin(x)cos(x) + cos(x)sin(2x).

Using the identity sin(2x) = 2sin(x)cos(x), we can substitute in for sin(2x):

\(sin(x) + sin(2x) + sin(3x) = sin(x)(2 - 2sin^2(x)) + 2sin(x)cos(x) + cos(x)(2sin(x)cos(x)).\)

Combining like terms:

sin(x) + sin(2x) + sin(3x) = 2sin(x) - 2sin^3(x) + 2sin(x)cos(x) + 2sin(x)\(cos^2(x).\)

Factoring out 2sin(x):

\(sin(x) + sin(2x) + sin(3x) = 2sin(x)(1 - sin^2(x) + cos(x) + cos^2(x)).\)

Using the identity \(sin^2(x) + cos^2(x) = 1:\)

sin(x) + sin(2x) + sin(3x) = 2sin(x)(1 + cos(x)).

This matches the expression on the right side of the identity: sin(2x)(1 + 2cos(x)).

Therefore, we have verified the identity sin(x) + sin(2x) + sin(3x) = sin(2x)(1 + 2cos(x)).

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Answer:

3+2 = 22 +30=  59 1/2

(x + c)2 = d or (x – c)2 = d. = (c * d)(x) = 4x^3 + 18x^2 - 10x

X=1+2

Step-by-step explanation:

sorry if wrong was every confused

Answer: the answers should be B and D

Step-by-step explanation:

so basically, this is just simplifying

B is the correct answer because the numerator 12, when divided by 4 is 3, and the denominator 32, when also diving by 4, is eight. This makes the two fractions equivalent.

Same goes for D, for if you diving the numerator and denominator by 2, you get answer choice D

it’s kind of a trial and error type problem and you have to test out all possibilities

hope this helps!

Answer:

B and D

Step-by-step explanation:

12/32 (if you divide them both by three) does not equal 4/10

12/32 fully simplified is 3/8

12/32 - subtracting is not simplifying, therefore, 10/30 is not correct

12/32 - both divided by two, a common factor, is 6/16, therefore, this answer is correct

12/32 - both of them divided by three equals 4/10.7 (rounded up to the nearest tenth), therefore, 4/9 is not a correct answer

12/32 - both divided by six equals 2/5.3 (rounded down to the nearest tenth), therefore, 2/6 is not a correct answer

a) For chi-squared distribution with v=3 degrees of freedom, the statistic that can be constructed using Xi's is:

X2 = Σ i=1 3 (Xi − i)2 / 3.

X2 has chi-squared distribution with 3 degrees of freedom.

b) For t-distribution with v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

T = (X1 − 1) / [(X2/2)0.5].

T has t-distribution with 2 degrees of freedom.

c) For F-distribution with v1=1 and v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

F = [(X1 − 1)/1] / [(Σi=2 to 3 Xi2) / 2].

F has F-distribution with 1 and 2 degrees of freedom.

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The value of t-score for a 99.8% confidence interval is 3.467 if we take a sample of size 25.

The range of values created around a sample estimate of a population parameter is known as a confidence interval. It is a means to put a number on the level of uncertainty surrounding a sample estimate. Confidence intervals are employed for drawing conclusions about the population from a sample. They are frequently employed in research investigations and data analysis and are a crucial instrument in statistical analysis.

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Solution:

To calculate the t-score, you would need to know the degrees of freedom, which is equal to the sample size minus 1 (in this case, 25 - 1 = 24). You would then look up the t-score in a t-table or use a t-distribution calculator with a confidence level of 99.8% and the appropriate degrees of freedom.

And looking in t-table we found out answer to be 3.467

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The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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Answer:

31.7 min

Step-by-step explanation:

Given that;

N(t) = Noe^kt

No = amount of radioactive isotope initially present

N(t) = amount of radioactive isotope present at time t

t = time taken

k = decay constant

5.25 = 14e^-k16

5.25/14 = e^-k16

0.375 = e^=k16

ln(0.375) = =-16k

k = ln(0.375)/-16

k = 0.0613 min^-1

So time taken for 2 mg to remain;

2 = 14e^-0.0613t

2/14 = e^-0.0613t

0.1429 = e^-0.0613t

ln(0.1429) = -0.0613t

t = ln(0.1429)/-0.0613

t = 31.7 min

There are 15 available courses and every student enrolls into 5 courses.

No greater than 10 courses that are unique to them and not shared with any other student.

To prove that there are 2 students who have 3 common courses, we have to take the steps;

Using the Pigeonhole principle, we have;

The principle of pigeonhole states  that if there are k pigeonholes and n pigeons and the value of n is greater than that of k, there must exist at least one pigeonhole containing more than one pigeon.

Then, we have;

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The linear equation is 45x+50

Linear equation is the equation having the degree 1

Given that the charge per computer repair service  is $50

The charge per hour of work is $ 45

We need to show the linear equation that  expresses the total amount of money Charlie earns per computer is y

So , Let the number of hours be x

Therefore, the Charlie working hours charge will be 45x

The total amount of money Charlie earns per computer is y

Therefore the linear equation will be

y = 50+45x  

Where y = Total amount of money

x =  number of hours

Hence the linear equation is y = 45x+50

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The answer is D. 2 over 5

Step-by-step explanation:

Took the test.

Using the simplex method, the optimal solution for the given linear programming problem is x = 2, y = 2, z = 0, with the maximum objective value of P = 10.



a. To rewrite the formulation in standard form, we need to replace the inequalities with equality constraints and introduce non-negative variables. Let's assume x, y, and z as the non-negative variables:

Maximize P = 3x + 2y + 4z

Subject to:2x + y + z + s1 = 8

x + 2y + 3z + s2 = 10

x, y, z ≥ 0

b. Utilizing the linear programming simplex method, we can solve the above formulation. After setting up the initial tableau, we perform iterations by selecting a pivot element and applying the simplex algorithm until an optimal solution is reached. The algorithm involves row operations to pivot the tableau until all coefficients in the objective row are non-negative. This ensures the optimality condition is satisfied, and the maximum value of P is obtained.

To provide a brief solution within 120 words, we determine the optimal solution by applying the simplex method to the above formulation. After performing the necessary iterations, we find that the maximum value of P occurs when x = 2, y = 2, z = 0, with P = 10. Therefore, the maximum value of P is 10, and the solution for the given problem is x = 2, y = 2, and z = 0.

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