What is the slope of the line tangent to the curve square root (x) +square root (y) = 2 at the point ( 9/4, 1/4 )? (photo attached of answer choices)

Answer:

Step-by-step explanation:

For x intercept:

0 = x−2

x = 2

For y intercept:

y = x−2

y = 0 -2

y = -2

For x intercept:

0 = -3x-6

6 = -3x

x = -2

For y intercept:

y= -3x-6

y = -3(0)-6

y = -6

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then the sum of digits of K is 9

Let the sets be

A =  {1, 2, 3, 4, 5, 6, 7, 8, 9}

B = {1, 2, 3, 4, 5}

C = {4, 5, 6, 7, 8, 9}

Then

B ∩ C = {4, 5}

Subsets of B ∩ C = {4}, {5}, {4,5}, {}

If we exclude the null set then the subsets remaining will be {4}, {5}, {4,5}

No. of elements in A = 9

No. of subsets of A = \(2^9\)

No. of elements in B = 5

No. of subsets of B = \(2^5\)

No. of elements in C = 6

No. of subsets of C = \(2^6\)

If we subtract the no. of subsets of B and C from the no. of subsets of A we get the no. of subsets of A that are not the subsets of B or C

But the null set will be subtracted twice

Also as the subsets of B ∩ C excluding null set will be subtracted twice

Therefore, total number of subsets of A not the subsets of B or C

\(k=2^9-2^5-2^6+1\\k=512-32-64-2\\\\k=414\)

The sum of the digits of k=9

The complete question is-

If the numbers of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} that are subsets of neither {1, 2, 3, 4, 5} nor {4, 5, 6, 7, 8, 9} is K, then find the sum of digits of K.

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The relationship between x and y is represent as:

Since, the relationship is linear.

The standard form of equation of line is:

Consider any two set x and y values from the given relationship.

Let (-2, 10) and (-1,7.5)

The equation of the linear relationship between x and y is:

y = -2.5(x + 2) + 10

Now, to check that the point (9, -17.5) lies on the represented relationship between x and y

Substitute x = 9 and y = -17.5 in the equation y = -2.5(x + 2) + 10

y = -2.5(x + 2) + 10

-17.5 = -2.5(9 + 2) + 10

-17.5 = -2.5(11) + 10

-17.5 = -27.5 + 10

-17.5 = -17.5

Thus, LHS = RHS

Hence the point (9, -17.5) lie on the given linear relationship between x and y.

Answer: The point (9, -17.5) lie on the given linear relationship between x and y.

The Stafford loan will have a higher balance of $36.53 at the time of repayment.

The correct option is C.

The formula:

PV = PMT/i[1 - {1/(1+i)ⁿ]

PV denotes the loan sum.

PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)

To compare the balances of the two loans at the time of repayment, we need to calculate the total amount owed for each loan.

For the Unsubsidized Stafford Loan:

The total loan amount is $6,720, and the annual interest rate is 3.99%, compounded monthly.

Therefore, the monthly interest rate is 3.99% / 12 = 0.3325%. The loan has a grace period of 6 months, so interest will not start accruing until 6 months after graduation.

The loan will be repaid over a period of 10 years, or 120 months.

Using the formula for the future value of an annuity, the total amount owed for the Unsubsidized Stafford Loan is:

FV = PMT x [(1 + r)ⁿ - 1] / r

where PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

We can solve PMT using a loan repayment calculator, such as the one found on bankrate.com, and we get a monthly payment of $73.80. Plugging this into the formula, we get:

FV = $73.80 x [(1 + 0.003325)¹¹⁴ - 1] / 0.003325

FV = $9,222.41

Therefore, the total amount owed for the Unsubsidized Stafford Loan at the time of repayment is $9,222.41.

For the PLUS Loan:

The loan amount is $7,241.17, and the annual interest rate is 4.99%, compounded monthly. Therefore, the monthly interest rate is 4.99% / 12 = 0.4158%. Interest starts accruing immediately, and the loan will be repaid over a period of 10 years, or 120 months.

Using the same formula, the total amount owed for the PLUS Loan is:

FV = PMT x [(1 + r)ⁿ- 1] / r

Again, using a loan repayment calculator, we get a monthly payment of $78.93. Plugging this into the formula, we get:

FV = $78.93 x [(1 + 0.004158)^120 - 1] / 0.004158

FV = $9,258.94

Therefore, the total amount owed for the PLUS Loan at the time of repayment is $9,258.94.

Comparing the two loan amounts, we see that the Unsubsidized Stafford Loan will have a higher balance of $36.53 ($9,222.41 - $9,258.94) at the time of repayment.

Therefore, the answer is:

The Stafford loan will have a higher balance of $36.53 at the time of repayment.

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Answer:

27/7

Step-by-step explanation:

First, note that 3 6/7 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

3 = whole number

6 = numerator

7 = denominator

To convert mixed number 3 6/7 to improper fraction, you follow these steps:

Multiply the whole number by the denominator

3 × 7 = 21

Add the product from Step 1 to the numerator

21 + 6 = 27

Write answer from Step 2 over the denominator

27/7

The mixed number 3 6/7 converted to improper fraction is therefore :

27/7

Answer:

27/7

Step-by-step explanation:

The best way to represent histograms is by decreasing to increasing order.

The mean is the arithmetic mean and is calculated by adding a group of numbers and dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Given the values:

50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45

We have that:

(22+24+28+28+30+31+31+32+32+35+36+37+38+41+42+42+44+44+45+46+46+47+47+49+50)/25=37.88.

The average age that a large construction company wants to know is 38.

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Answer:

The original price of the shirt was Ksh 500 and it was sold for Ksh 550.

The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.

To find the percentage discount, we can use the formula:

percentage discount = (discount ÷ original price) × 100%

percentage discount = (-50 ÷ 500) × 100%

percentage discount = -10%

Therefore, the percentage discount is 10%.

The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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Answer: d. Triangle with angle measures: 8·, 17·, and 152·

Step-by-step explanation: i did the test

The triangle not possible is option

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Let us find the sum of the angles for each triangle given.

(a) Triangle with angle measures: 26°, 19°, and 135°·

Sum = 26° + 19° + 135° = 180°

(b)Triangle with angle measures: 14°, 27°, and 139°·

Sum = 14° + 27° + 139° = 180°

(c) Triangle with angle measures: 9°, 18°, and 153°·

Sum = 9° + 18° + 153° = 180°

(d) Triangle with angle measures: 8°, 17°, and 152°·

Sum = 8° + 17° + 152° = 177°, which is not equal to 180°.

Hence the option (d) is not possible.

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Answer:

Step-by-step explanation:

You want points A(-4, 0), B(0, -1) and C(-3, -3) reflected across the y-axis and translated left 5 and up 2.

The reflection across the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

The translation adds the translation vector to the reflected coordinates.

  (x, y) ⇒ (x -5, y +2) . . . . . . translation (by itself)

Then the result of both transformations is ...

  (x, y) ⇒ (-x -5, y +2)

For a number of points, this arithmetic is conveniently accomplished by a calculator. The result is ...

Answer:

A. True.

Step-by-step explanation:

To get the standard error of the mean, you need to do the sample standard deviation over the square root of the number of samples, n.

In this case, n = 100. The standard deviation is 12. To get the SAMPLE standard deviation, you do the population standard deviation over the square root of n. That is 12 / sqrt(100) = 12 / 10 = 1.2.

So, to get the standard error: 1.2 / sqrt(100) = 1.2 / 10 = 0.12.

The standard error of the mean is, indeed, 0.12, so the statement is A. True.

Hope this helps!

Total number of students = 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30

The probability that a student is female given that it is a junior is computed as follows:

The probability that a student is female and junior is:

The probability that a student is a junior is:

Finally, The probability that a student is female given that it is a junior is:

Answer:

slope intercept: y=5x-7

Step-by-step explanation:

first you need slope: y2-y1/x2-x1

-12-3/-1-2=

-15/-3=

5

then plug into this formula: y-y1=m(x-x1)

y-3=5(x-2)

y-3=5x-10

y=5x-7

A two-sample z-test for a difference in population proportions is the appropriate method for analyzing the results.

Z-test is a statistical test often utilizes to find the difference in mean. It is coupled with variances and sample size to find the appropriate results. It is a hypothetical test where normal distribution is seen.

z-test holds numerous advantages such as it indicates difference in small size groups making it more usable. Moreover, it is also reliable in non-normal distribution of data and is efficient while taking multiple groups in a single analysis. The question has two different popular proportion and hence the two sample z-test will suitable to compare the means.

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The order in which the operations are done when simplifying a exponential expression is 1)Addition and subtraction 2)Multiplication and division 3)exponents.

To solve an exponential expression, first we will use the addition and subtraction of all the expressions.

then we will use the operations of multiplication or division and finally we will use the operation of exponent.

Exponentiation to real powers for positive real numbers can be defined in two comparable ways: either by extending its rational powers to reals both by continuity or by utilizing the base's logarithm and really the exponential function.

These formulas for real exponents result in positive real numbers and are consistent with the identities and criteria stated above for integer exponents. Because the second formulation clearly generalizes to complex exponents, it is used more commonly.

Because the limit that characterizes the exponential value converges with any complex value of x, it is possible to extend the definition of the exponential function from the real numbers toward any complex argument z. Despite being often used to describe exponentiation for complex bases and exponents, this extended exponential function nevertheless satisfies the exponential identity.

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Answer:

Step-by-step explanation:

The correct answer is true. If you know that the relationship between quantities is proportional, you can use proportions to find missing quantities.

The vertex form of the equation is y = 3(x + 2)^2 - 5

The equation is given as:

y = 3x^2 + 12x + 7

Set to 0

3x^2 + 12x + 7 = 0

Subtract 7 from both sides

3x^2 + 12x = -7

Divide through by 3

x^2 + 4x = -7/3

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

Take the coefficient of x

k = 4

Divide by 2

k/2 = 2

Square both sides

(k/2)^2 = 4

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

So, we add 4 to both sides of x^2 + 4x = -7/3

x^2 + 4x + 4 = -7/3 + 4

Express as perfect square

(x + 2)^2 = -7/3 + 4

Multiply through by 3

3(x + 2)^2 = -7 + 12

Evaluate

3(x + 2)^2 = 5

Subtract 5 from both sides

3(x + 2)^2 - 5 = 0

Rewrite as

y = 3(x + 2)^2 - 5

Hence, the vertex form of the equation is y = 3(x + 2)^2 - 5

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Answer:

Option C, neither.

Step-by-step explanation:

Here we have the table:

x: -10    -3    4    11

y:   1      6    30   120

This means that if our function is f(x), then:

f(-10) = 1

f(-3) = 6

f(4) = 30

f(11) = 120

We want to know if this represents a linear equation or an exponential equation or neither.

First, let's try with a linear equation.

We know that a linear equation can be written as:

f(x) = a*x + b

Then let's input the known values and let's see if this equation works.

We can use two of the known points to get:

f(-10) = 1 = a*-10 + b

f(4) = 30 = a*4 + b

With these equations, we can find the value of a and b, once we find these values, we can see if the equation also works for the other two points.

1 = a*-10 + b

30 = a*4 + b

First, we need to isolate one of the variables in one of the equations.

I will isolate b in the first one:

b = 1 + a*10

Now we can replace this in the other one to get:

30 = a*4 + 1 + a*10

30 = 1 + a*14

30 - 1 = a*14

29 = a*14

29/14 = a = 2.07

and using the equation b = 1 + a*10 we can find the value of b:

b = 1 + 2.07*10 = 1 + 20.7 = 21.7

Then the equation we get is:

f(x) = 2.07*x +  21.7

Now we need to see if this works for the other two points:

for x = -3, we need to get: f(-3) = 6

f(-3) = 2.07*-3 + 21.7 = 15.49

We did not get the value we expected, then we already know that the relationship is not linear.

Now let's see if the relationship can be exponential.

An exponential function is written as:

f(x) = A*(r)^x

Let's do the same as above, let's use two of the known points to find the values of A and r

f(-3) = 6 = A*(r)^(-3)

f(4) = 30 = A*(r)^4

Now we have the system of equations:

30 = A*(r)^4

6 = A*(r)^(-3)

If we take the quotient of these two equations, we get:

(30/6) = (A*(r)^4)/( A*(r)^(-3))

5 = (r^4)*r^3 = r^(4 + 3) = r^7

(5)^(1/7) = r = 1.258

And the value of A is given by:

30 = A*(1.258)^4

30/( (1.258)^4 ) = 11.98

Then the exponential equation is something like:

f(x) = 11.98*(1.258)^x

Now let's see if this equation also works for the other two points:

for x = -10, we should get f(-10) = 1

Let's see that:

f(-10) = 11.98*(1.258)^(-10) = 1.2

And for x = 11 we should get f(11) = 120

f(11) =  11.98*(1.258)^(11) = 149.6

So we get values closer to the ones we should get, but not the exact ones, so this is not an exponential relation.

Then the correct option is C, neither.

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer:

52

Step-by-step explanation:

7 · 5 + (4² + 3) - 12 + 10

7 · 5 + (16 + 3) - 12 + 10

7 · 5 + 19 - 12 + 10

35 + 19 - 12 + 10

52

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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Answer:

Step-by-step explanation:

To find Bianca's walking speed, we need to divide the distance she walks by the time it takes her to walk that distance. We can do this by converting both the distance and time to the same unit of measure.

Since 1 hour is equal to 60 minutes, 1/3 of an hour is equal to 1/3 * 60 minutes = 20 minutes. Now that we have the distance in miles and the time in minutes, we can divide the distance by the time to find Bianca's walking speed.

5/6 of a mile is equal to 5/6 * 1 mile = 0.83 miles. So, Bianca's walking speed is 0.83 miles / 20 minutes = 0.0415 miles per minute. To convert this to miles per hour, we can multiply by the conversion factor of 60 minutes per hour. This gives us a walking speed of 0.0415 miles/minute * 60 minutes/hour = 2.49 miles per hour. So, Bianca's walking speed is 2.49 miles per hour.

Answer:

Step-by-step explanation:

The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

As per option (B),

Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.

Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.

Sarah rides her bike = 3/4 × 8/9

Therefore, this problem can be solved by performing the above multiplication.

Hence, the correct answer would be an option (B).

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The minimum value of \($\|\mathbf{v}\|$\) is zero.

The minimum value of \($\|\mathbf{v}\|$\) is zero, as it is the distance between the origin and a point on the line. To solve this problem, the formula \($\|\mathbf{v}\| = \sqrt{x^2 + y^2}$\) can be used, where x and y are the coordinates of the point on the line. Since the equation of the line is \($\dbinom{10}{3} \dbinom{-2}{1}t$\), the coordinates of the point on the line can be found by substituting \($t = 0$: $x = 10 \cdot 0 - 2 \cdot 0 = 0$, and $y = 3 \cdot 0 + 1 \cdot 0 = 0$\) . Substituting these values into the formula for \($\|\mathbf{v}\|$ gives $\|\mathbf{v}\| = \sqrt{0^2 + 0^2} = 0$\). Therefore, the minimum value of \($\|\mathbf{v}\|$\) is zero.

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