Evaluate the expression when a=6 and b=4.
b +9a​

Radians are a unit of measurement for angles used in mathematics and physics. They are defined as the ratio between the length of an arc of a circle and the radius of that circle.

One of the most important benefits of using radians to measure angles is that they simplify calculations involving angles, making them easier to work with.

Additionally, they allow for a more elegant and unified approach to mathematical and physical problems involving angles. So, in short, the word "radian" might be associated with concepts such as circles, arcs, and the measurement of angles in mathematics and physics.

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Answer:

70.5

Step-by-step explanation:

Set of Data (Prioritized):

31, 43, 47, 58, 63, 68, 69, 72, 77, 84, 84, 84, 94, 97

To find the median:

(69 + 72) ÷ 2

= 70.5

Therefore, the median is equal to 70.5.

Answer:

She buys 5 boxes of popcorn and 6 boxes of candy

Step-by-step explanation:

this is because 5 times 4.00 is 20$ and 2.50 times 6 is 15$

15 + 20 is 35

so your answer is 5 boxes of popcorn and 6 boxes of candy

hope this helped :D

Answer:

B

Step-by-step explanation:

If she spent 35$ and got 1 more candy and popcorn that only leaves a single option

Answer:

the discount amount is $13

Step-by-step explanation:

the discount percent is 27.08%

Answer:

27%

Step-by-step explanation:

$48 - $35 = $13

$13 : $48 = x% : 100%

x = ($13 × 100%) ÷ $48 ≈ 27%

Answer:

Where's the graph?

Step-by-step explanation:

Answer:

need a picture.

Step-by-step explanation:

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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The 99% confidence limit will be option B which is (45, 55)

90% confidence limits for the population mean are (46,54)

mean = 46+54 / 2 = 50.

the margin of error E = 54-46/2 = 4

For 90% Confidence Z- Critical value is = 1.645

But the margin of error

E = ZS/√n

4=(1.645)S/√n

S/√n = 4 / 1.645

= 2.4316

For 95% confidence Z-critical value is 1.96

A 95% confidence interval is = mean ± E

(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316

= 50+ 4.7660

= 45.2340, 54.7660

= (45, 55)

Hence the correct option is B which is (45, 55) as the 99% confidence limit.

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x2-5x+4}

Step-by-step explanation:

It would take approximately 6 minutes to travel through the thickest oceanic crust at a speed of 100 km/hr.

To determine the time it would take to travel through the thickest oceanic crust at a speed of 100 km/hr, we need to know the thickness of the oceanic crust.

The oceanic crust is the outermost layer of the ocean floor and is generally thinner than the continental crust. On average, the thickness of the oceanic crust ranges from 5 to 10 kilometers (km). However, the thickness can vary depending on the specific location and geological factors.

Assuming we consider the thickest part of the oceanic crust, which could be up to 10 km thick, we can calculate the time it would take to travel through it at a speed of 100 km/hr.

Using the formula Time = Distance / Speed, we can determine the time as follows:

Time = (Thickness of Oceanic Crust) / (Speed)

Time = 10 km / 100 km/hr = 0.1 hr

Converting 0.1 hour to minutes, we have:

Time = 0.1 hr * 60 min/hr = 6 minutes

The correct answer is D. 6 minutes. This calculation is based on the assumption that we are considering the thickest part of the oceanic crust, which is approximately 10 km thick. It's important to note that the actual thickness of the oceanic crust can vary, and the time required would depend on the specific thickness encountered during the journey.

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Answer:

C) The graph opens down and the vertex is a maximum.

Step-by-step explanation:

Just took the quiz on K12, good luck! :)

Option (C) will be the correct option.

         f(x) = ax² + bx + c

         Vertex of the parabola is represented by \([-\frac{b}{2a}, f(\frac{b}{2a})]\)

         And the sign of the leading coefficient decides the opening of the

         parabola.

         For positive sign of 'a' → Parabola will open upwards

         For negative sign of 'a' → Parabola opens downwards

Quadratic function given in the question is,

f(x) = -4x²+ 6x - 7

Leading coefficient → (-4)

Negative sign represents the opening of the parabola downwards.

And the vertex will be a maximum.

           Therefore, Option (C) will be the correct option.

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When a distribution is shown as a symmetrical bell-shaped curve then the mean, median, and mode are equal i.e., option (a) is correct.

A symmetrical bell-shaped curve, also known as a normal distribution or Gaussian distribution, is characterized by its symmetry around the mean.

In this type of distribution, the mean, median, and mode all coincide at the center of the curve.

This means that the central tendency measures, such as the mean (average), median (middle value), and mode (most frequent value), are all equal.

Option (a) states that the mean, median, and mode are equal, which aligns with the properties of a symmetrical bell-shaped curve. This equality occurs because the data is evenly distributed on both sides of the mean, resulting in a balanced distribution.

Options (b) and (d) suggest that the mean is either less than or greater than the median and mode, which does not hold true for a symmetrical distribution.

In a symmetrical distribution, the mean is located at the center of the data, and the median and mode share the same value as the mean.

Option (c) mentions moderate uniformity, but a symmetrical bell-shaped curve does not specifically indicate uniformity. Uniformity refers to a distribution where all data points have equal probability, resulting in a flat line.

In contrast, a symmetrical bell-shaped curve indicates a normal distribution with the majority of data concentrated around the mean, gradually decreasing towards the tails.

Therefore, based on the given options, option (a) is the correct conclusion when the distribution is shown as a symmetrical bell-shaped curve.

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The interest portion of the first payment is $495.38.

a) The loan amount can be calculated as follows;

Total cost of the house = $176,000

Down payment (10% of $176,000) = $17,600

Therefore, the loan amount is calculated as follows;

Loan amount = Total cost of the house - Down payment

= $176,000 - $17,600= $158,400

b)The monthly payments on the loan can be calculated as follows;

The monthly payment can be calculated using the following formula; Monthly payment = \([i(PV)] / [1 - (1 + i)^_-n]\)

Where; i = Interest rate per month

= 0.0375 / 12

= 0.003125P

= Loan amount

= $158,400n

= Number of months

= 30 × 12= 360

Substitute the values

Monthly payment = \([0.003125(158,400)] / [1 - (1 + 0.003125)^_-360]\)

Monthly payment = $733.77 (rounded to two decimal places)

Therefore, the monthly payments are $733.77.

c) To find out how much of the first payment is interest, we can use the following

formula; Interest = Loan amount × Monthly interest rate Substitute

the values;

Monthly interest rate = Annual interest rate / 12

= 0.0375 / 12

= 0.003125

Interest = $158,400 × 0.003125

Interest = $495.38

(rounded to two decimal places)

Therefore, the interest portion of the first payment is $495.38.

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Answer:

Step-by-step explanation:

The function is f(x) = x²

Transformation steps

1. Reflection across the x-axis:

2. Translation 3 units to the left:

3. Translation 4 units up:

The new function is:

Correct choice is B

Step-by-step explanation:

11.

Area of rectangle = 408 in²

Length = 3x-2 and width = x

The area of a rectangle is given by :

A = lb

(3x-2)x = 408

x = 12 inch and x = -11.33 in

Neglecting negative value,

The width of rectangle = 12 inch

The length of rectangle = 3x-2 = 3(12)-2 = 34 inch

12.

Base of triangle = 2x+2

Height = x

The area of a triangle is given by :

\(A=\dfrac{1}{2}bh\\\\600=\dfrac{1}{2}\times (2x+2)x\\\\600=(x+1)x\)

x = 24 cm and x = -25 cm

Neglecting negative value, x = 24 cm

Base = 2x+2 = 2(24)+2 = 50 cm

Hence, this is the required solution.

Answer:

The answer is (Not Proportional)

Step-by-step explanation:

The pair of ratios 0.08/0.2 and 0.2/0.8 are proportional.

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

To check whether two ratios are proportional, we can simplify each ratio to lowest terms and then see if they are equal.

For the first ratio 0.08/0.2, we can simplify both the numerator and denominator by a factor of 0.04:

0.08/0.2 = (0.08/0.04) / (0.2/0.04) = 2/5

For the second ratio 0.2/0.8, we can simplify both the numerator and denominator by a factor of 0.2:

0.2/0.8 = (0.2/0.2) / (0.8/0.2) = 1/4

Now we can see that the simplified ratios are equal:

2/5 = 0.4 and 1/4 = 0.25

Since the simplified ratios are equal, the pair of ratios 0.08/0.2 and 0.2/0.8 are proportional.

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The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

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A statistically significant negative correlation coefficient of r = -0.91 was obtained from a sample of n = 30. This indicates a strong and significant negative relationship between the variables.

The researcher conducted a correlation analysis and found a correlation coefficient (r) of -0.91, which indicates a strong negative relationship between the variables under investigation. The negative sign indicates that as one variable increases, the other variable tends to decrease, and vice versa.

The statistical significance of the correlation coefficient is crucial in determining whether the observed relationship is likely to be due to chance or if it truly exists in the population. In this case, the report should highlight that the obtained correlation coefficient is statistically significant.

To establish statistical significance, the researcher likely conducted a hypothesis test, such as a t-test or a permutation test, to determine the probability of obtaining a correlation coefficient as extreme as -0.91 under the null hypothesis of no correlation. Since the obtained correlation coefficient is statistically significant, it suggests that the observed negative relationship is unlikely to be a result of chance and provides evidence for a genuine association between the variables in the population from which the sample was drawn.

Reporting this finding is important for conveying the strength and significance of the negative relationship to the readers, providing valuable insights for further analysis and interpretation of the variables under investigation.

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Answer:

2X + 5

Step-by-step explanation:

1st. 2 × 1 + 5 => 7

2nd. 2 × 2 + 5 => 7

3rd. 2 × 3 + 5 => 7

4th. 2 × 4 + 5 => 7

5th. 2 × 5 + 5 => 7

6th. 2 × 6 + 5 => 7

Xth. 2 × X + 5 => 2X + 5

Answer:

f(x)2x+5

Step-by-step explanation:

Answer:

on 14th day

Step-by-step explanation:

...........

Step-by-step explanation:

8 1/3 = 25/3

= 8.3333

8 1/3 = 8 + 1/3

= 8 + 0.3333

= 8.3333

Answer:

8⅓ = 8.3

Step-by-step explanation:

Solving Fraction to decimal

8 * 3 + 1 /3

= 25/3

= 8.3

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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The compensating variation is $13.52.

The compensating variation is the amount of money that Greg would need to be compensated for a price increase in order to maintain his original level of utility. In this case, Greg's utility function is u = x^0.38x^0.962. His income is $83.00, and he faces these prices: (P1, P2) = (4.00, 1.00). If the price of x increases by $1.00, then the new prices are (P1, P2) = (5.00, 1.00).

To calculate the compensating variation, we can use the following formula:

CV = u(x1, x2) - u(x1', x2')

where u(x1, x2) is Greg's original level of utility, u(x1', x2') is Greg's new level of utility after the price increase, and CV is the compensating variation.

We can find u(x1, x2) using the following steps:

Set x1 = 83 / 4 = 20.75.

Set x2 = 83 - 20.75 = 62.25.

Substitute x1 and x2 into the utility function to get u(x1, x2) = 22.13.

We can find u(x1', x2') using the following steps:

Set x1' = 83 / 5 = 16.60.

Set x2' = 83 - 16.60 = 66.40.

Substitute x1' and x2' into the utility function to get u(x1', x2') = 21.62.

Therefore, the compensating variation is CV = 22.13 - 21.62 = $1.51.

To two decimal places, the compensating variation is $13.52.

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Answer:

\(\frac{1}{x^{\frac{5}{3}}}\)

Step-by-step explanation:

\(\frac{-5}{3}=-\frac{5}{3}\\x^{-\frac{5}{3}}\\x^{-\frac{5}{3}}=\frac{1}{x^{\frac{5}{3}}}\\\frac{1}{x^{\frac{5}{3}}}\)

➲ Hope this helps.

The volume of the triangular prism is 255 cm³.

What is a triangular prism?

A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.

Here, we have

Given: The dimensions of a triangular prism are shown in the diagram.

We have to find the volume of the triangular prism in cubic centimeters.

Volume = (area of base) × (height of prism)

Volume = bh/2 × H

Volume = (8.5 cm)(6 cm)/2 × 10 cm

Volume = 255 cm³

Hence,  the volume of the triangular prism is 255 cm³.

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The length of the shortest straight  is approximately 28.01 ft.

What is the right triangle?

A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".

To find the length of the shortest straight beam,we can use the Pythagorean theorem.

Let's denote the length of the beam as L and  a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.

Using the Pythagorean theorem,

\(L^2 = (28 ft)^2 + (1 ft)^2\)

Simplifying the equation:

\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)

\(L = \sqrt{785}ft\)

Calculating the value of L:

L ≈ 28.01 ft

Therefore, the length of the shortest straight beam  is approximately 28.01 ft.

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The annual continuous (relative) growth rate would be approximately 9.53%(D).

To find the annual continuous growth rate, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

A = final amount

P = initial amount

r = continuous growth rate

t = time

We know that the population grows by 10% each year, so the growth rate (r) can be calculated as follows:

r = ln(1 + 10%) = ln(1.1) ≈ 0.0953

Converting the growth rate to a percentage gives us approximately 9.53%. So D is correct option.

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False. Not every algebraic extension of Q (the rational numbers) is a finite extension. There exist algebraic extensions of Q that are infinite.

An algebraic extension is an extension field where every element is a root of some polynomial with coefficients in the base field. In the case of Q, an algebraic extension is formed by adjoining algebraic numbers to Q.

One example of an infinite algebraic extension of Q is the field of algebraic numbers. This field consists of all the roots of polynomials with rational coefficients. Since there are infinitely many polynomials with infinitely many roots, the field of algebraic numbers is an infinite algebraic extension of Q.

Therefore, it is not true that every algebraic extension of Q is a finite extension. Some algebraic extensions of Q can be infinite.

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The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

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