A survey found that the ratio of students who play intruments to those who do not was 7/20 of the students do not play an instrument 440 surveyd how many students surveyd play an instument

Answer:

-2x^2-6x-15=0

Step-by-step explanation:

Shift the 15 to the other side to get ax^2+bx+c

-2x^2-6x-15=0

Answer:

36 degrees

Step-by-step explanation:

A decagon is a 10 sided polygon. We can tell this because the prefix "deca-" stands for ten. To find the exterior angles of a regular polygon you can do 360 divided by the number of sides. Since there are 10 sides on a decagon, the equation is 360/10, which equals 36 degrees.

On the other hand, you can find the interior angles by using a different equation. The sum of the angles in a polygon is equal to 180(n-2) where n is the number of sides. So, a decagon has 1440 degrees. Then, to find the measure of each individual angle divide this number by the number of sides, 10. Thus, each angle is 144 degrees.

You can use this information to check the original answer. The interior angle plus the exterior angle should equal 180. Since 144+36=180, we know that the answer is correct.

Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

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According to Thales theorem :

\( \frac{AB}{AE} = \frac{BC}{ED} \\ \)

\( \frac{2}{2 + 5.2} = \frac{s}{6} \\ \)

\( \frac{2}{7.2} = \frac{s}{6} \\ \)

\( \frac{1}{3.6} = \frac{s}{6} \\ \)

\( \frac{s}{6} = \frac{1}{3.6} \\ \)

Multiply sides by 6

\(6 \times \frac{s}{6} = 6 \times \frac{1}{3.6} \\ \)

Simplification

\(s = \frac{6}{3.6} \\ \)

\(s = \frac{6}{36 \times {10}^{ - 1} } \\ \)

\(s = \frac{6 \times {10}^{1} }{36} \\ \)

\(s = \frac{6 \times 2 \times 5}{6 \times 2 \times 3} \\ \)

6 s and 2 s are simplify

\(s = \frac{5}{3} \\ \)

\(s≈1.67\)

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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Answer:

yes

Step-by-step explanation:

A basis for the space of 2x2 lower triangular matrices is \(\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)\).

Lower triangular matrices resemble the following:

\(\left[\begin{array}{ccc}a&0\\b&c\end{array}\right]\)

We can write it like this:

\(a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\)

This demonstrates the set's

\(\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)\)

covers the set of lower triangular matrices with dimensions 2x2. Moreover, these are linearly independent, so attempting to

\(a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]\)

leads to

\(\left[\begin{array}{ccc}a&0\\b&c\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]\)

which results in a = b = c = 0 right away. As there is no other way to

\(a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]\)

, these matrices are linearly independent if a = b = c = 0.

Since

\(\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)\)

they serve as a foundation by spanning the collection of 2x2 lower triangular matrices and being linearly independent.

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Answer:

B=28

Step-by-step explanation:

From standard normal distribution table, The minimum score among those who received scholarships was approximately 710.

To find the minimum score among those who received scholarships, we need to find the corresponding z-score using the standard normal distribution table.

Given that 2.28 percent of the students who had the highest scores received scholarships, we can find the z-score corresponding to this percentile. The z-score represents the number of standard deviations the score is above or below the mean.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to the 2.28th percentile is approximately -2.04.

Now, we can calculate the minimum score by using the z-score formula:

z = (x - mean) / standard deviation

Rearranging the formula, we can solve for x (the minimum score):

x = z * standard deviation + mean

Substituting the values:

x = -2.04 * 75 + 500

x ≈ 710

Therefore, the minimum score among those who received scholarships was approximately 710.

The minimum score among those who received scholarships was approximately 710 on the mathematics part of the SAT at UTC.

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Answer:

21 / 252

Step-by-step explanation:

Recall : nCr = n! ÷ (n-r)!r!

The total possible outcome ; 5 questions out of 10

10C5 = 10! ÷ 5!5! = (10*9*8*7*6)÷(5*4*3*2*1) = 252

Required outcome :

All 5 questions set being from the 7 questions covered and 0 from the 3 left uncovered

7C5 * 3C0

7C5 = 7! ÷ 2!5! = (7*6) ÷ (2*1) = 21

3C0 = 3! ÷ 3!0! = 1

Probability = required outcome / Total possible outcomes

P(All 5 questions prepared for appears) :

[7C5 * 3C0] ÷ 10C5

(21 * 1) / 252

= 21 / 252

29 Nickels

15 Dimes

Hope this is helpful!

Answer:

0.5

Step-by-step explanation:

-1+3(10-12)^3/-16

-1+3(-2)^3/-16

-1+(-24)/-16

.5

Answer:

y = x^2

Explanation:

The correct answer is c. I and III only.

Explanation:

i. As x → [infinity], f(x) → 2: This statement is true. As x approaches infinity, the exponential term -2^(-x - 2) approaches 0, and the constant term 2 remains. Therefore, the function approaches 2 as x approaches infinity.

ii. The x-intercept is (-2, 0): This statement is false. To find the x-intercept, we set f(x) = 0 and solve for x:

0 = -2^(-x - 2) + 2

2^(-x - 2) = 2

Taking the logarithm of both sides:

(x + 2) = log2(2)

(x + 2) = 1

x = -3

Therefore, the x-intercept is (-3, 0), not (-2, 0).

iii. The function is an example of exponential decay: This statement is true. The function f(x) = -2^(-x - 2) + 2 is a decreasing function as x increases. As x becomes larger, the exponential term -2^(-x - 2) becomes smaller, causing the function to approach 2, which is the horizontal asymptote. This behavior is characteristic of exponential decay.

In summary, based on the given options, statements i and iii are true, while statement ii is false. Therefore, the correct answer is c. I and III only.

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Answer:

15 is 50% of 30

and 75% of 20

Answer:

y = 7

Step-by-step explanation:

See the picture below.

Answer:

15/2= 7 1/2 =7.5

Step by step

Step 1 of 2: Add.

Add

5 and 2 over 165

2

16

+ 2 and 3 over 82

3

8

= 120 over 16

120

16

Step 1 of 2: Add, sub-step a: Convert mixed number to improper fraction.

Convert mixed number to improper fraction

5 and 2 over 165

2

16

= ( 5 × 16 ) over 16

5 × 16

16

+ 2 over 16

2

16

= ( 80 + 2 ) over 16

80 + 2

16

= 82 over 16

82

16

Step 1 of 2: Add, sub-step b: Convert mixed number to improper fraction.

Convert mixed number to improper fraction

2 and 3 over 82

3

8

= ( 2 × 8 ) over 8

2 × 8

8

+ 3 over 8

3

8

= ( 16 + 3 ) over 8

16 + 3

8

= 19 over 8

19

8

Step 1 of 2: Add, sub-step c: Find common denominator.

Find common denominator

82 over 16

82

16

+ 19 over 8

19

8

= ( 82 × 1 ) over ( 16 × 1 )

82 × 1

16 × 1

+ ( 19 × 2 ) over ( 8 × 2 )

19 × 2

8 × 2

= 82 over 16

82

16

+ 38 over 16

38

16

16 is the least common multiple of denominators 16 and 8. Use it to convert to equivalent fractions with this common denominator.

Step 1 of 2: Add, sub-step d: Add.

Add

82 over 16

82

16

+ 38 over 16

38

16

= ( 82 + 38 ) over 16

82 + 38

16

= 120 over 16

120

16

Step 1 of 2: Add.Hide

Step 2 of 2: Simplify.

Simplify

120 over 16

120

16

= 15 over 2

15

2

= 7 and 1 over 27

1

2

Step 2 of 2: Simplify, sub-step a: Reduce fraction to lowest terms.

Reduce fraction to lowest terms

120 over 16

120

16

= ( 120 ÷ 8 ) over ( 16 ÷ 8 )

120 ÷ 8

16 ÷ 8

= 15 over 2

15

2

8 is the greatest common divisor of 120 and 16. Reduce by dividing both numerator and denominator by 8.

Step 2 of 2: Simplify, sub-step b: Convert improper fraction to mixed number.

Convert improper fraction to mixed number

15 over 2

15

2

= 7 and 1 over 27

1

2

15 ÷ 2 = 7 remainder 1

Problem 1

PMT = 505.76 = monthly payment

k = monthly interest rate in decimal form

k = 0.043/12 = 0.003583333 (approximate)

n = 5*12 = 60 months

PVOA = present value of ordinary annuity

PVOA = PMT * ( 1 - (1+k)^(-n) )/k

PVOA = 505.76 * ( 1 - (1+0.003583333)^(-60) )/0.003583333

PVOA = 27,261.436358296

When rounding to the nearest dollar, we get $27,261

Your teacher made a mistake in choosing the formula. S/he mixed up present value ordinary annuity with annuity due. The (1+k) portion at the end is ignored. I rewrote the 1/( (1+k)^n ) sub-portion as (1+k)^(-n) to avoid a bit of clutter.

--------

To type this into excel we will write

=PV(0.043/12,5*12,505.76,0,0)

That will produce the result of -27,261.44. The negative is to indicate a cash outflow.

Don't forget about the equal sign up front when writing excel formulas.

=====================================================

Problem 2

L = loan amount = 23099

k = interest rate per month = 0.051/12 = 0.00425 exactly

n = number of months = 5*12 = 60 months

PMT = monthly payment

PMT = (Lk)/(1 - (1 + k)^(-n) )

This formula is the result of solving PVOA = PMT * ( 1 - (1+k)^(-n) )/k for "PMT". The PVOA value is the loan amount in this case.

Let's plug in the values mentioned

PMT = (Lk)/(1 - (1 + k)^(-n) )

PMT = (23099*0.00425)/(1 - (1 + 0.00425)^(-60) )

PMT = 436.965684557303

PMT = 437 when rounding to the nearest whole number

--------

To do this in excel, we type in

=PMT(0.051/12,5*12,23099,0,0)

The output should be -436.97 which rounds to -437.

The value is negative to represent a cash outflow, but your teacher mentions to post the answer as a positive value.

Answer:

200=4hrs=10 of the machines

200=4hrs

300=xhrs

Cross multiply

200×xhrs = 300×4hrs

X=1200/200

X= 6 hours

ANSWERS

• tan(θ) > 1:, θ ,∈, {(π/4,, ,π/2) ∪ (5π/4, 3π/2)}

• tan(θ) < -1: ,θ ,∈, {(π/2, 3π/4) ∪ (3π/2, 7π/4)}

EXPLANATION

tan(θ) is a periodic function, that repeats its values between -π/2 and π/2.

When θ is close π/4, tan(θ) goes to infinity. The same happens for 5π/4, π/2 and 3π/2

Let's see the graph:

For θ between π/4 and π/2, the value of the tangent is more than 1. This is also true for θ between 5π/4 and 3π/2.

Then, when θ is between π/2 and 3π/4, and when it's between 3π/2 and 7π/4, tan(θ) is less htan -1.

If we want to increase  the width of a confidence interval , we need to increase the confidence interval which will increase our z value

What is confidence interval?

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.

E=zs√n. The margin of error is represented by the quantity E. The margin of error is equal to the confidence interval's width divided by two. Occasionally, confidence intervals are expressed as x±E, for instance, 9.95±0.43.

Thus if we want to increase  the width of a confidence interval , we need to increase the confidence interval which will increase our z value

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Multiple regression offers a more comprehensive and nuanced analysis by considering the influence of multiple predictors, capturing complex relationships, controlling for confounding variables, and enhancing predictive capabilities.

A study using multiple regression has several advantages over a study using bivariate correlation:

Multivariate analysis: Multiple regression allows for the inclusion of multiple predictor variables, which enables the examination of their individual contributions while controlling for the effects of other variables. This helps to identify the unique influence of each predictor on the outcome variable, considering their interrelationships.

Complex relationships: Multiple regression can capture complex relationships between variables by accounting for their combined effects. Bivariate correlation can only assess the linear relationship between two variables, whereas multiple regression can handle non-linear relationships and interactions between predictors.

Control of confounding variables: Multiple regression enables the control of confounding variables by including them as predictors in the model. By controlling for potential confounders, the relationship between the predictor and outcome variables can be more accurately assessed, reducing the likelihood of spurious associations.

Increased predictive power: Multiple regression can improve the predictive power of the model by incorporating multiple predictors. By considering multiple factors simultaneously, it can provide a more comprehensive understanding of the factors influencing the outcome variable and better predict its values.

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Magnitude of vector u = √(5² + (-9)² + 0²) = √106 Magnitude of vector v = √(5² + 1² + (-3)²) = √35,Therefore,cos(θ) = (-4) / (√106) (√35)θ = cos⁻¹(-4 / (√106) (√35))= 2.38 radians (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Given vectors are u

= 4i - 4j and v

= -4i + 4j + k.The angle between the vectors is radians.To find the angle between two vectors u and v, we use the following formula;cos(θ)

= (u.v) / |u| |v|where θ is the angle between vectors u and v, u.v is the dot product of vectors u and v, and |u| and |v| are the magnitudes of the respective vectors u and v.Dot Product: u.v

= (4)(-4) + (-4)(4) + (0)(1)

= -16 -16

= -32Magnitude of vector u

= √(4² + (-4)² + 0²)

= √32

Magnitude of vector v

= √((-4)² + 4² + 1²)

= √33 Therefore,cos(θ)

= (-32) / (√32) (√33)θ

= cos⁻¹(-32 / (√32) (√33))

= 2.18 radians (rounded to the nearest hundredth).The given vectors are u

= √5i - 9j and v

= √5i + j - 3k.

The angle between the vectors is radians.To find the angle between two vectors u and v, we use the following formula;cos(θ)

= (u.v) / |u| |v|where θ is the angle between vectors u and v, u.v is the dot product of vectors u and v, and |u| and |v| are the magnitudes of the respective vectors u and v.Dot Product: u.v

= (√5)(√5) + (-9)(1) + (0)(-3)

= 5 - 9 = -4.Magnitude of vector u

= √(5² + (-9)² + 0²)

= √106

Magnitude of vector v

= √(5² + 1² + (-3)²)

= √35

Therefore,cos(θ)

= (-4) / (√106) (√35)θ

= cos⁻¹(-4 / (√106) (√35))

= 2.38 radians (Do not round until the final answer. Then round to the nearest hundredth as needed.)

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Given that the second student chosen is a girl, the probability that both students are female is 0.175.

The occurrence of likely events is referred to as probability. It is the branch of mathematics concerned with numerical estimates of the likelihood of an event occurring or a statement being true.

Probability is nothing but likelihood of something is to occur. When we are unsure about the outcome of an event, we can discuss the probabilities of certain outcomes—how likely they are.

The probability of selecting a girl from the class is

\(= \frac{Number\ of\ girls}{ Total\ number\ of\ students}= \frac{14}{26}\\\\= \frac{7}{13}\)

It is known that the one of the chosen student from 2 students is girl, the probability of having both girls will be:

\(= \frac{7}{16} * \frac{6}{15}\\\\= 0.175\)

Hence, the probability is 0.175.

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Your question is incomplete, here is the complete question.

Your statistics class has 26 students in it - 14 girls and 12 boys.Your teacher uses a calculator to select two students at random to solve a problem on the board. Given that the second student chosen is a girl, what is the probability that the first student was also a girl?

Answer:

y=25,000(0.89)^6

Step-by-step explanation:

Answer:

a: y= 25,000(0.89)^6

Step-by-step explanation:

9514 1404 393

Answer:

  (0, 2), (5, 5)

Step-by-step explanation:

The w-intercept is the constant in the equation, so you know immediately that (x, w) = (0, 2) is one point on your graph.

Since the value of x is being multiplied by 3/5, it is convenient to choose an x-value that is a multiple of 5. When x=5, we have ...

  w(5) = (3/5)(5) +2 = 3+2 = 5

So, (x, w) = (5, 5) is another point on your graph.

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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