Convert the following base-ten numerals to a numeral in the indicated bases. a. 861 in base six b. 2157 in base nine C. 131 in base three a. 861 in base six is six

Answer:

480

Step-by-step explanation:

Using the tangent of the angle, the value of θ is 25°

Trigonometric ratios are mathematical relationships between the angles of a right triangle and the ratios of the lengths of its sides. These ratios are used extensively in trigonometry to analyze and solve problems involving angles and distances.

In the given problem, the figure have the opposite side and adjacent of the right-angle triangle.

Using the tangent of the triangle;

tanθ = opposite / adjacent

tanθ = 33/72

Let's inverse of the tangent.

θ = tan⁻¹(33/72)

θ = 24.62

θ = 25°

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Step-by-step explanation:

you did not show us the graph, and your problem description is a bit gibberish - I am sure there are some important parts missing.

therefore it is impossible to answer this.

Answer:

Step-by-step explanation:

Sample Space

off  even numbers

= {2,4,6,8,10}.

There are 5 outcomes in the sample space,

Answer:

Step-by-step explanation:

bro this question is wrong needs more data

Answer:  (choice B) 12

Step-by-step explanation:

In an isosceles triangle, two sides are equal in length. From the information given, the triangle has sides with lengths \(10\), \(13\), and \(13\), with a base of \(x\). Since it's isosceles, the two equal sides are \(13\) each, and the base is \(10\).

To find the value of \(x\), you can use the Pythagorean theorem. Let \(x\) be the height of the triangle, and then we have:

\[ x^2 + \left(\frac{10}{2}\right)^2 = 13^2 \]

\[ x^2 + 25 = 169 \]

\[ x^2 = 144 \]

\[ x = 12 \]

So, the correct answer is \(x = 12\), which matches Choice B.

1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Answer:

I don't see any equations.

If Jane and Sarah share an amount of £63 and Jane receives "5/9" of  money, then the amount of money Sarah receives is £28..

The total amount that needs to be shared between Jane and Sarah is = £63,

We know that , Jane receives "5/9" of the total amount,

Which means , Jane receives = (5/9)×63 = £35,

The total-sum of money is = £63,

So, We can write,⇒ Total money = Jane + Sarah,

Substituting the values ,

We get,

⇒ 63 = 35 + Sarah,

⇒ Sarah = 63 - 35 = £28.

Therefore, Sarah's share of money is = £28.

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the answer would be x=5.075

Answer:

$357

Step-by-step explanation:

Probability of yellow disk will be selected is  \(\frac{4}{5}\). probability \(\frac{5}{25}\) that a yellow disk will be randomly selected from the bag.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

Given

n(S) = 25

a. Probability of yellow disk will be selected is O is

n(E) = 25 - 5 = 20

P(E) = \(\frac{n(E)}{n(S)}\) =  \(\frac{20}{25}\) = \(\frac{4}{5}\)

b. It is the probability \(\frac{5}{25}\) that a yellow disk will be randomly selected from the bag.

Hence, Probability of yellow disk will be selected is  \(\frac{4}{5}\). probability \(\frac{5}{25}\) that a yellow disk will be randomly selected from the bag.

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Answer: The square root of 216 is equal to approximately 6.485281.

Step-by-step explanation:

The square root of 216 is equal to the number that, when multiplied by itself, gives 216. The value of the square root of 216 can be found using several methods, including estimation, the long division method, and a calculator. Here, I'll provide a step-by-step explanation using estimation.

Step 1: Estimate the value of the square root.

One way to estimate the value of the square root of 216 is to find two perfect squares that are close to 216, and whose square roots are therefore close to the square root of 216. In this case, the perfect squares closest to 216 are 144 (12^2) and 225 (15^2). Since 216 is closer to 144, the square root of 216 is likely to be closer to 12 than to 15.

Step 2: Refine the estimate.

To refine the estimate of the square root of 216, we can average the two closest perfect squares and their square roots. In this case, the average of 12 and 15 is 13.5, and this is a better estimate of the square root of 216 than either 12 or 15 alone.

Step 3: Improve the estimate using a more precise method.

One method for finding an even more precise estimate of the square root of 216 is to use the Newton-Raphson formula for finding square roots. This formula involves repeatedly applying the following equation:

x_n+1 = (x_n + n/x_n) / 2,

where x_n is the nth estimate of the square root, and n is the number whose square root we are trying to find (in this case, n = 216). We can start with an initial estimate, such as x_0 = 13.5, and iterate the formula until the estimate converges to a desired level of precision.

Step 4: Use a calculator or other tools to find the exact value.

Finally, we can use a calculator or computer program to find the exact value of the square root of 216 to as many decimal places as desired. The exact value of the square root of 216 is equal to approximately 6.485281.

9 miles per gallon of gas is used in his car.

The standard volume and capacity for measuring liquids is the gallon.The word gallon is shortened to gal.Currently, there is only one definition for the gallon in the imperial system and two that is dry and liquid in the US customary system.

Here the given information is as,

Car travels = 144 miles

Tank hold gas = 16 gallons

So, for miles per hour,

= 144 / 16

= 9 miles / gallon

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Answer:

See below

Step-by-step explanation:

\(p=5j\)

\(q=2i\)

\(p+q=5j+2i=2i+5j\)

\(p-q=5j-2i=-2i+5j\)

\(2p-3q=2(5j)-3(2i)=10j-6i=-6i+10j\)

The results obtained by central limit theorem are given below-

μ = 170 customers per day

σ = 45 customers per day

n = 31

\(\begin{aligned}&\mu_{x}=170 \\&\sigma_{x}=8\end{aligned}\)

The Central Limit Theorem proves that the distribution of a sample means of size n can be estimated to the normal distribution with mean  (μ) and standard deviation (σ) for one random normally distributed variable X, with mean (μ) and standard deviation (σ);

\(s=\frac{\sigma}{\sqrt{n}}\)

This Central Limit Theorem may also be applied to skewed variables if n is at least 30.

She observes that the rival business averages 170 clients per day, with a standard deviation of 45 clients.

Thus, \(\mu=170, \sigma=45\)

Let's say she selects a random sampling of 31 days.

So, n = 31

Now, the mean is according to the Central Limit Theorem is

\(\mu_{x}=170\), and

standard deviation = \(\sigma_{x}=\frac{45}{\sqrt{31}}=8\)

Therefore, by using central limit theorem the data is obtained as,

μ = 170 customers per day

σ = 45 customers per day

n = 31

\(\begin{aligned}&\mu_{x}=170 \\&\sigma_{x}=8\end{aligned}\)

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The complete question is-

A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary:

μ = _____customers per day

σ = _____customers per day

n = ____

\(\mu_{x}\) =____

\(\sigma_{x}\) = ____

The leap pattern of the frog is up 2 steps then back 1 step. To reach 10th step she have to take 9 leaps up.

Let represent leaps up with positive number and leaps back with negative number.

Hence, the movement of the little green frog can be written as:

2 - 1 + 2 - 1 + 2 - 1 + ....

Notice, that every 4 leaps (both up and back) she reaches 2 steps.

2 - 1 + 2 - 1  = 2

Hence, after 4 x 4 = 16 leaps she will reach the 8th steps. The last leap in this instant is leap back. Hence, the next leap will be leaps up 2 steps, and she reaches the 10th steps.

In every 4 leaps there are 2 leaps up.

Therefore, she have to leaps up 2 x 4 + 1 = 9 leaps up.

You can also write all her leaps to reach the 10th steps:

2 - 1 + 2 - 1 +    2 - 1 + 2 - 1  +    2 - 1 + 2 - 1  +   2 - 1 + 2 - 1   + 2

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The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6

Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.

Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.

Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.

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The value of economic output measured in an economy over a year is known as real GDP. It is an adjusted for inflation measure. IT uses base year prices to compute GDP growth. Therefore, just the change in output is included and the change in price is not included.

In the base year, a green pepper cost $2. Red pepper cost $3 per pound.

Real GDP

= 150 × $2 + 60 × $3

= $300 + $180

= $480

The real GDP in the current year is $480.

The real GDP this year if the base year was last year is $480.

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The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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The expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

As per the question, we can write the expression as:

(t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9)

Using product notation, we can write this as:

Π⁷k =1 \((t^k - 9)\)

where Π represents the product of terms, k is the index of the product, and the subscript 7 indicates that the product runs from k = 1 to k = 7.

Therefore, the expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

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The simplified form of the expression, 6x²-23x+15, is (6x - 5)(x - 3)

The simplified form of the expression, x²-9, is (x + 3)(x - 3)

From the question, we are to simplify the given expression by factoring

The given expression is

6x² - 23x + 15

Factoring

6x² - 23x + 15

6x² - 18x - 5x + 15

6x(x - 3) -5(x - 3)

(6x - 5)(x - 3)

∴ The simplified form of the expression is (6x - 5)(x - 3)

We are to simplify

x² - 9

By difference of two squares, we have that

a² - b² = (a + b)(a - b)

x² - 9 can be expressed as

x² - 3²

Thus,

Using difference of two squares

x² - 3² = (x + 3)(x - 3)

Hence, the simplified form of the expression is (x + 3)(x - 3)

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Answer:

the angle is 245°

Step-by-step explanation:

that is a pentagon, (a shape with 5 sides)

we know 4 of the angles in the pentagon

the sum of those 4 angles is

58°+100°+112°+25°=295°

to find a shapes total amount of °, the equation is (n-2)x180°

(5-2)x180°

=540°

540°-295°=245°

x=245°

Answer: Pretty sure it's A

Answer:

D. Reflect across Y axis and translate 2 units up

Step-by-step explanation:

Move PQR to XZY

a.  this expression will give us the linearization of the ball's position at t = 12. b. the approximate height of the ball at t = 11.5 seconds based on the linearization.

(a) The linearization of the ball's position at t = 12 can be found using the given information.

The linearization of a function at a specific point is given by the equation:

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

In this case, the position of the ball is the function, and we are interested in finding its linearization at t = 12 seconds. The given information tells us that at t = 12 seconds, the ball has a downward velocity of 381 feet per second and is 2000 feet above the ground.

Let's assume that the position function of the ball is denoted by p(t), where t represents time. We know that the ball is dropped from rest, so its initial velocity is 0. Therefore, we can integrate the velocity function to find the position function:

p(t) = ∫[0 to t] v(u) du

Since the ball is dropped from a plane, the acceleration due to gravity is acting in the downward direction, and we can assume that the velocity function is given by:

v(t) = -32t + c

where c is a constant. To find the value of c, we can use the given information. At t = 12 seconds, the velocity of the ball is given as 381 feet per second. Substituting this into the velocity function:

381 = -32(12) + c

c = 765

Now, we have the velocity function v(t) = -32t + 765. Integrating this function gives us the position function:

p(t) = -16t^2 + 765t + k

where k is another constant. To determine the value of k, we use the fact that at t = 12 seconds, the ball is 2000 feet above the ground:

2000 = -16(12)^2 + 765(12) + k

k = -1080

Therefore, the position function of the ball is:

p(t) = -16t^2 + 765t - 1080

To find the linearization of the ball's position at t = 12, we need to evaluate the position function at t = 12 and find its derivative at that point:

L(12) = p(12) + p'(12)(t - 12)

L(12) = (-16(12)^2 + 765(12) - 1080) + (-32(12) + 765)(t - 12)

Simplifying this expression will give us the linearization of the ball's position at t = 12.

(b) To find the height of the ball at t = 11.5 seconds using the linearization, we substitute t = 11.5 into the linearization equation obtained in part (a). By evaluating this expression, we can determine the approximate height of the ball at t = 11.5 seconds based on the linearization.

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Answer: D

Step-by-step explanation: We first need to solve the inequality.

First subtract 10 from both sides to get -x < -8.

Now divide both sides by -1, but watch out.

If you multiply or divide both sides of an inequality by

a negative number, you must switch the direction of the inequality sign.

So we have x > 8.

Start with an open dot at 8 and draw and arrow to the right.

We use an option dot since x is greater than but not equal to 8.

So option D is your answer.

Answer:

The correct answer is D

Step-by-step explanation:

Answer: A

Step-by-step explanation:  

Take the root of both sides and solve.

Answer:

A

Step-by-step explanation:

It just is

Answer:

The first 3 terms of the sequence \(t(n)=-2n+7\) are:

\(5, 3, 1\)

Step-by-step explanation:

Given the sequence

\(t(n)=-2n+7\)

Here \(n\) represents any term number in the sequence

Determining the first term

substitute n = 1 in the sequence to determine the first term

\(t(n)=-2n+7\)

\(t(1)=-2(1)+7\)

\(t(1)=-2+7\)

\(t(1) = 5\)

Determining the 2nd term

substitute n = 2 in the sequence to determine the 2nd term

\(t(n)=-2n+7\)

\(t(2) = -2(2) + 7\)

\(t(2) = -4 + 7\)

\(t(2) = 3\)

Determining the 3rd term

substitute n = 3 in the sequence to determine the 3rd term

\(t(n)=-2n+7\)

\(t(3) = -2(3) + 7\)

\(t(3) = -6 + 7\)

\(t(3) = 1\)

Therefore, the first 3 terms of the sequence \(t(n)=-2n+7\) are:

\(5, 3, 1\)

Answer:

570 meters

Step-by-step explanation:

\(\frac{8}{152} :\frac{30}{y}\)

y × 8 = 152 × 30

8y = 4560

8y ÷ 8 = 4560 ÷ 8

y = 570

A p-value for correlation which is statistically significant implies the correlation is due to random chance. The correct solution to this is False.

A p-value for correlation which is statistically significant implies that it is unlikely that the observed correlation is due to random chance alone. In other words, it suggests that there is evidence to support the presence of a true correlation between the two variables being studied. The p-value is a measure of the strength of evidence against the null hypothesis (i.e., that there is no correlation between the two variables), and a smaller p-value indicates stronger evidence against the null hypothesis.

Interpretation of the intercept: The intercept in a linear regression model represents the value of the dependent variable when all independent variables are equal to zero. It is the value of the dependent variable when there is no effect of the independent variable(s) on it. For example, in a regression model predicting height based on age, the intercept would represent the expected height of a person at age zero (which is not a realistic scenario).

Interpretation of a residual: A residual is the difference between the actual observed value of the dependent variable and the predicted value of the dependent variable based on the regression model. It represents the part of the dependent variable that the model was not able to explain. A positive residual means that the actual value is greater than the predicted value, while a negative residual means that the actual value is smaller than the predicted value.

Interpretation of r-squared: R-squared is a measure of how much of the variation in the dependent variable is explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. Specifically, it represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. For example, if r-squared is 0.75, it means that 75% of the variability in the dependent variable is explained by the independent variable(s) in the model.

Interpretation of the slope: The slope in a linear regression model represents the change in the dependent variable that is associated with a one-unit increase in the independent variable, holding all other variables constant. It reflects the average change in the dependent variable for each unit change in the independent variable. For example, in a regression model predicting height based on age, the slope would represent the average change in height for each additional year of age.

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