for any positive numbers a, b, and d, with b ≠ 1, logb(a)+logb(d)

Answer:

sdgsehseh

Step-by-step explanation:

sehsdhsehsdhs

The cost of three points for the homebuyers is $739.80.

To calculate the cost of three points for the homebuyers, we need to determine the value of each point and then multiply it by three.

Given:

Loan amount: $137,000

Interest rate without points: 5.05%

Interest rate with points: 4.87%

The difference between the two interest rates is the value of one point.

Interest rate difference = 5.05% - 4.87% = 0.18%

To find the value of one point, we calculate 0.18% of the loan amount:

Value of one point = 0.18% * $137,000

Value of one point = 0.0018 * $137,000

Value of one point = $246.60

Now, to determine the cost of three points, we multiply the value of one point by three:

Cost of three points = $246.60 * 3

Cost of three points = $739.80

The price of three points for the homebuyers is therefore $739.80.

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Given

The center of the circle is (7,-2).

And, it passes through (-10,0).

To find the equation of the circle.

Explanation:

It is given that,

The center of the circle is (7,-2).

And, it passes through (-10,0).

Then, the standard form of the circle is given by,

Since it passes through (-10,0).

Then,

Hence, the equation of the circle is,

Sum of the interior angle of any triangle must equal to 180 degrees thus :

\(53 + 90 + t = 180\)

\(143 + t = 180\)

\(t = 37\)

Thus angle T has a measure of 37° .

Answer: 37

Explanation: Angle S is a right triangle because ST is tangent to circle Q.
180 - 90 - 53 = 37

Consider the selection of a thirteen card bridge hand. This is a combination.

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Dempster's rule of combination is a formula for combining two or more belief functions. When the combined belief functions are based on different or "independent" sources of information, the formula intuitively equates to pooling of evidence.

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Answer:

\(y=60\textdegree\)

Step-by-step explanation:

The Tangent-Secant Interior Angle Measure Theorem states that the measure of an angle formed by a tangent and a secant of a circle at the point of tangency is equal to half of the measure of its intercepted arc.

Therefore, \(y=\frac{1}{2} *120\textdegree = \bf 60\textdegree\). Hope this helps!

Answer: the simple interest rate of 4.5%

Step-by-step explanation:

What Is Simple Interest?

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to specific loans. It's also the type of interest that banks pay customers on their savings accounts.

The formula to determine simple interest is an easy one. Just multiply the loan's principal amount by the interest rate by the term.

This type of interest usually applies to automobile or short-term loans, although some mortgages use this calculation method.

What is compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest. It is the result of reinvesting interest, adding it to the loaned capital rather than paying it out, or requiring payment from the borrower so that interest in the next period is then earned on the principal sum plus previously accumulated interest. Compound interest is standard in finance and economics.

Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period, so there is no compounding. The simple annual interest rate is the interest amount multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with the interest rate not adjusted for inflation, which goes by the same name).

Answer:

26

Step-by-step explanation:

9=x+1

5=10÷3

9=x+1

5=3.333°

Now you need to find scale factor (sf)

5÷3.333°=1.5

SF=1.5

9÷3.333=2.7

2.7-1=1.7

x=1.7

Answer:

  x = 5

Step-by-step explanation:

Given PQRS ~ UVWT and PQ = 5, RS = 9, UV = 10/3, WT = x+1, you want the value of x.

Corresponding side lengths of similar polygons are proportional. This means ...

  WT/UV = RS/PQ

  (x+1)/(10/3) = 9/5 . . . . . . . . . . . substitute given values

Multiplying by 10/3 gives ...

  x +1 = (10/3)(9/5) = 6

  x = 5 . . . . . . . . . subtract 1

Answer:

3x+2z =8. 2x=4

Step-by-step explanation:

Answer: Symmetric property

Step-by-step explanation:

This is the Symmetric property.

The Symmetric property states: If x=y, then y=x. This fits the question, since 3x=2z, then 2z=3x.

Hope this helps!! :)

Please let me know if you have any questions

Calculating the mean is simply finding the average of data set.

Mean = Total number of children/ Total number of household

=9 /36

= 1/4

=0.25

This means that 1 out of 4 families have 1 child in the total numbers of 36 household.

Answer:

Within 52 weeks, the amount of water in the two fish tanks will be the same.

Step-by-step explanation:

First, let's make the two equations equal to each other by placing an equal sign.

832 - 5x = 1040 - 9x

Now, that they are equal to each other, we can solve for x.

Okay, so we can move -5x to the other side by adding both sides with 5x.

832 = 1040 - 4x

Then, subtract 1040 from both sides to move it to the other side.

832 - 1040 = -208

-208 = -4x

Lastly, divide both sides by -4 to get the value of x.

-208/-4 = 52

x = 52

The value is a z value of 5, which corresponds to a very unlikely sample mean given the mean and standard deviation of the population, which is not given in any of the options.

Based on the given information, we can assume that we have a normal distribution of sample means. This distribution is called the sampling distribution, and it represents all possible sample means that could be obtained from the same population.

The mean of the sampling distribution is the same as the population mean, which is 30 in this case. The standard deviation of the sampling distribution is calculated by dividing the population standard deviation by the square root of the sample size. Therefore, we have:

Standard deviation of sampling distribution = 8 / sqrt(n)

We don't know the sample size (n) in this case, so we cannot calculate the exact standard deviation of the sampling distribution. However, we do know that a sample mean of 40 corresponds to a z value of:

z = (sample mean - population mean) / (standard deviation / sqrt(n))

We can rearrange this formula to solve for the sample size (n):

n = (standard deviation / (sample mean - population mean)) ^ 2

Plugging in the given values, we get:

n = (8 / (40 - 30)) ^ 2 = 64

Therefore, a sample mean of 40 corresponds to a sample size of 64. The corresponding z value can be calculated using the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(n))

z = (40 - 30) / (8 / sqrt(64)) = 5

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Answer:

The number that is multiplied repeatedly is called the base.

Answer:

2

Step-by-step explanation:

The easiest way to explain slope is the units up between each point on the line, divided by the units across. For this graph:

(-5,-6) and (0,4)

(y2 - y1) / (x2-x1)

4-(-6) = 4+6 = 10

0-(-5) = 0+5 = 5

10/5 = 2

Hope this helped!

a) The mean for the given data is 11.44

b) The median for the given data is 11

c) The mode for the given data is 11

d) The maximum score received by a student is 18

e) The minimum score received by a student is 3

f) The range for the given data is 15

g) The interquartile range for the given data set {12, 6, 9, 5, 11} is 6

h) The third quartile for the given data set  {0, 8, 14, 17, 7} is 15.5

i) The third quartile for the given data set {14, 11, 9, 3, 12} is 13

j) The interquartile range for the given data set {3, 8, 9, 11, 5}  is 6

The interquartile range is a measure of statistical dispersion in descriptive statistics, which is the spread of the data. The IQR is also known as the middle 50% spread, the fourth spread, or the H-spread.

a) Mean=(12+8+11+10+6+7+10+13+14+15+9+18+17+15+3+11+11)/18

=11.44

Therefore, mean=11.44

b) Median= n is even

Then,

((n/2 )th +((n/2)+1)th)/2

=(11+11)/2

=11

Therefore, median=11

c) Mode= The number that is repeated highest number of times

Mode=11

Therefore, mode=11

d) The maximum score received by a student is 18

e) The minimum score received by a student is 3

f) Range=maximum-minimum

=18-3

=15

Therefore, Range=15

g) Median=9

Q₁=(5+6)/2=5.5

Q₃=(11+12)/2=11.5

Interquartile range=|Q₃-Q₁|

=|11.5-5.5|

=6

The interquartile range for the given data set {12, 6, 9, 5, 11} is 6

h) Median=10

Q₃=(14+17)/2=15.5

The third quartile for the given data set  {0, 8, 14, 17, 7} is 15.5

i) Median=11

Q₃=(12+14)/2=13

The third quartile for the given data set {14, 11, 9, 3, 12} is 13

j) Median=8

Q₁=(3+5)/2=4

Q₃=(9+11)/2

Interquartile range=|Q₃-Q₁|

=|10-4|

=6

The interquartile range for the given data set {3, 8, 9, 11, 5}  is 6

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Answer: 18.68

Step-by-step explanation:

Answer:

41,257

Step-by-step explanation:

100,000

-

58,743

-------------

41,257

The amount that is needed to reach the goal is $41257 if the annual fundraising goal of a college is $100,000. so far $58,743 has been raised.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The annual fundraising goal of a college is $100,000.

Let x be the amount that is needed to reach the goal.

The linear equation in one variable can be framed as follows:

x + 58,743 = 100,000

x = 100,000 - 58,743

x = $41257

Thus, the amount that is needed to reach the goal is $41257 if the annual fundraising goal of a college is $100,000. so far $58,743 has been raised.

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Answer:

\(\displaystyle{L=\dfrac{(49\pi^2+64)\sqrt{49\pi^2+64}-512}{192}}\)

Step-by-step explanation:

Length of polar curve has formula of:

\( \displaystyle{L = \int_{ \theta_1 }^{ \theta_2} \sqrt{ {r}^{2} + \left( \dfrac{dr}{d \theta} \right)^2 } \: d \theta}\)

From power rule, we know that:

\( \displaystyle{ \dfrac{dr}{d \theta} = 2 \theta}\)

Therefore, substitute r, angles and its derivative in:

\(\displaystyle{L = \int_{0 }^{ \frac{7\pi}{4} }\sqrt{ { \theta}^{4} + \left( 2 \theta \right)^2 } \: d \theta} \\ \\ \displaystyle{L = \int_{0 }^{ \frac{7\pi}{4} }\sqrt{ { \theta}^{4} + 4 \theta^{2} } \: d \theta} \\ \\ \displaystyle{L = \int_{0 }^{ \frac{7\pi}{4} }\sqrt{ \theta^2(\theta^2+4)} \: d \theta} \\ \\ \displaystyle{L = \int_{0 }^{ \frac{7\pi}{4} } \theta \sqrt{ \theta^2+4}\: d \theta}\)

Let the following:

\(\displaystyle{u=\sqrt{\theta^2+4}\to u^2=\theta^2 + 4 \to 2u \: du = 2\theta \: d\theta \to u\: du=\theta \: d\theta}\)

Therefore, substitute in appropriate terms:

\(\displaystyle{L = \int_{0 }^{ \frac{7\pi}{4} } u \sqrt{ u^2}\: d u}\\\\\displaystyle{L = \int_{0 }^{ \frac{7\pi}{4} } u ^2\: d u}\)

Since we now use u-term as the interval, we have to substitute theta intervals in \(\displaystyle{u=\sqrt{\theta^2+4}}\) to find new intervals. Hence:

\(\displaystyle{u_{\theta_2}=\sqrt{\left(\dfrac{7\pi}{4}\right)^2+4} =\sqrt{\dfrac{49\pi^2}{16}+4} =\sqrt{\dfrac{49\pi^2}{16}+\dfrac{64}{16}} =\sqrt{\dfrac{49\pi^2+64}{16}}}\\\\\displaystyle{u_{\theta_1}=\sqrt{0^2+4}=\sqrt{4}=2}\)

Now we have our new interval of:

\(\displaystyle{L = \int_{2}^{ \sqrt{\frac{49\pi^2+64}{16}} } u ^2\: d u}\)

Then we can apply definite integration rule:

\(\displaystyle{L = \left[ \dfrac{u^3}{3}\right]_{2}^{ \sqrt{\frac{49\pi^2+64}{16}} } }\\\\\displaystyle{L= \dfrac{\left(\sqrt{\dfrac{49\pi^2+64}{16}\right)^3} }{ 3} - \dfrac{2^3}{3}}\\\\\displaystyle{L=\dfrac{\dfrac{49\pi^2+64}{16}\sqrt{\dfrac{49\pi^2+64}{16}}}{3}-\dfrac{8}{3}}\\\\\displaystyle{L=\dfrac{\dfrac{49\pi^2+64}{64}\sqrt{49\pi^2+64}}{3}-\dfrac{8}{3}}\\\\\displaystyle{L=\dfrac{(49\pi^2+64)\sqrt{49\pi^2+64}}{192}-\dfrac{8}{3}}\)

\(\displaystyle{L=\dfrac{(49\pi^2+64)\sqrt{49\pi^2+64}}{192}-\dfrac{512}{192}}\\\\\displaystyle{L=\dfrac{(49\pi^2+64)\sqrt{49\pi^2+64}-512}{192}}\)

And that’s the answer!

The lowest point of the cables above the bridge is 48 feet above the bridge.

The statement give us a parabola equation in standard form, the vertical distance of the lowest point above the bridge is determined by the y-coordinate of the vertex. Hence, the lowest point of the cables above the bridge is 48 feet above the bridge.

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Answer:

\(r = \frac{1}{84} c\)

Step-by-step explanation:

\(c = 2 \times 3 \times 14r\)

\(2 \times 3 \times 14r = 6 \times 14r = 84r\)

\(c = 84r = 84r = c\)

\(84r \div 84 = c \div 84\)

\(r = c \div 84\)

\(\boxed{\green{r = \frac{1}{84} c}}\)

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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To demonstrate that eᴬ is nonsingular for any diagonalizable matrix A, an explanation is needed regarding the properties of diagonalizable matrices, the definition of nonsingular matrices, and the properties of the exponential function.

For a diagonalizable matrix A, it can be expressed as A = PDP⁻¹, where P is the invertible matrix formed by the eigenvectors of A, and D is the diagonal matrix consisting of the eigenvalues of A.

Now, considering eᴬ, we have eᴬ = e^(PDP⁻¹). Using the properties of exponentials, we can rewrite this as eᴬ = Pe^D P⁻¹.

Since D is a diagonal matrix, e^D can be obtained by exponentiating each diagonal element. As the exponential function is well-defined for all real numbers, e^D will also be a diagonal matrix.

Since P and P⁻¹ are invertible matrices (since P consists of eigenvectors and P⁻¹ is its inverse), and e^D is a diagonal matrix with non-zero diagonal elements, the product Pe^DP⁻¹ is also nonsingular.

Therefore, eᴬ is nonsingular for any diagonalizable matrix A

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Answer:

$88.50

Step-by-step explanation:

118*0.75 = 88.50

Answer:88.50

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

13.7

Step-by-step explanation:

c^2 - b^2 = a^2

16.5^2 - 9.2^2 = a^2

272.25 - 84.64 = square root of a

square root of 187.61

= about 13.66 or 13.7

Answer:

9.2square +16.5square whole under root

Step-by-step explanation:

use a calculator sorry I don't have one on me

The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle

To find the length of the arc subtended by the angle's rays, we need to know the angle measure. Since we know that 1/360th of the circumference is 0.04 cm long, we can find the circumference by multiplying 0.04 cm by 360, which gives us 14.4 cm.

Now, we need to find the angle measure. Since the circle is centered at the vertex of the angle, the angle measures half the arc it subtends. Thus, we can find the angle measure by dividing the circumference by 2 and then multiplying by 1/360.

Angle measure = (14.4/2) x (1/360) = 0.02 radians

Finally, we can find the length of the arc subtended by the angle's rays by multiplying the angle measure by the radius of the circle.

Length of arc = 0.02 x radius


The length of the arc subtended by the angle's rays is 0.02 times the radius of the circle. The given information of 1/360th of the circumference being 0.04 cm long helped us find the circumference and subsequently the angle measure.

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To find one machine that does not work, you expected to buy 200 machines on average.

One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.

A company named Batco sells batteries.

And Batco claims that  99.5% of their batteries are in working order.

That means, 100 - 99.5 = 0.5% of their machines have defect.

0.5 as a fraction of 100% is 0.005.

To find the one machine that does not work;

Divide 1 by fraction of machines not working,

1 / 0.005

= 200

Therefore, you need to buy 200 machines.

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Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.

To determine the number of days it would take two computers to print personalized letters, the formula to use is given as follows:

1/Total Work = 1/Work of Computer A + 1/Work of Computer B

= 1/TimeTaken

In this question, Computer A takes 8 days to do the job, and Computer B takes 5 days to do the job.

Therefore, 1/Total Work = 1/8 + 1/5 = 0.25

Therefore, the total work would be equal to 1/0.25, which is equal to 4 days.

Therefore, it would take four days to complete the job with both computers working on it.

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The expression is equivalent to (x - 2)(x - 5)/(x - 4)(x - 1), as long as the denominators do not equal 0.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

We can begin by factoring the denominators of both fractions as follows:

\(x^{2}\)- x - 12 = (x - 4)(x + 3)

\(x^{2}\)- + 6x - 5 = (x - 1)(x + 5)

Substituting these expressions, the given expression becomes:

[(x - 1)(x-1)  \(x^{2}\)-+ (-6)]/[(x - 4)(x + 3)] * [(x + 5)/(x - 1)(x + 5x - 5)]

Simplifying, we can cancel out the (x - 1) and (x + 5) terms in the numerator and denominator:

[(x - 1) *  \(x^{2}\)- + (-6)]/[(x - 4)(x + 3)] * [1/(x - 5)]

Expanding the numerator:

( \(x^{3}\)-  \(x^{2}\)- - 6)/( \(x^{2}\)- - x - 12) * [1/(x - 5)]

Factoring the numerator:

( \(x^{2}\)- + x - 6)(x - 5)/( \(x^{2}\)- - x - 12)

Factoring again:

(x + 3)(x - 2)(x - 5)/(x - 4)(x + 3)(x - 1)

Canceling out the (x + 3) terms:

(x - 2)(x - 5)/(x - 4)(x - 1)

Therefore, the expression is equivalent to (x - 2)(x - 5)/(x - 4)(x - 1), as long as the denominators do not equal 0.

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