Solve an equation that can be used to determine the value of k.
(11k-23)
Y
Z
(5k - 3)°
(14k - 4)°
X W

The values are a. f(-3) = 7, b. f(a+3) = 2a² + 19a + 37, c. f(3a) = 18a² + 21a - 2, d. f(a+h) = 2a² + 4ah + 2h² + 7a + 7h - 2

What is a function?

A function is a mathematical relationship or rule that assigns a unique output value to each input value. It is a fundamental concept in mathematics and plays a central role in various branches, including calculus, algebra, and analysis.

To evaluate the given function at various values, we substitute the given values into the function and simplify the expression.

a. To find f(-3), we substitute -3 into the function: f(-3) = 2(-3)² + 7(-3) - 2 = 18 - 21 - 2 = 7.

b. To find f(a+3), we substitute a+3 into the function: f(a+3) = 2(a+3)² + 7(a+3) - 2. Expanding and simplifying the expression yields 2a² + 12a + 18 + 7a + 21 - 2 = 2a² + 19a + 37.

c. To find f(3a), we substitute 3a into the function: f(3a) = 2(3a)² + 7(3a) - 2. Simplifying the expression gives 18a² + 21a - 2.

d. To find f(a+h), we substitute a+h into the function: f(a+h) = 2(a+h)² + 7(a+h) - 2. Expanding and simplifying the expression yields 2a² + 4ah + 2h² + 7a + 7h - 2.

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Answer:

57

Step-by-step explanation:

95/5 x 3 = 57

Answer:

275 miles

Step-by-step explanation:

110/2=55

(2*110)+55

=275

Answer:

275 miles

Step-by-step explanation:

110×2=220

110÷2=55

220+55=275

To find the probability that 10 customers will arrive in a particular 15-minute period, we can use the Poisson distribution formula:

P(X = k) = (e^(-λ) * λ^k) / k!

Where λ is the mean arrival rate, which is 7 in this case, and k is the number of customers we're interested in, which is 10.

P(X = 10) = (e^(-7) * 7^10) / 10!

Calculating this expression will give us the probability that exactly 10 customers will arrive in a particular 15-minute period.

b. To find the probability that 10 or fewer customers will arrive in a particular 15-minute period, we need to sum up the probabilities of different arrival counts from 0 to 10.

P(X ≤ 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 10)

We can use the Poisson distribution formula for each value of k and sum them up to find the cumulative probability.

c. To find the probability of more than 10 customers arriving during a particular 15-minute period, we can calculate the complement of the probability of 10 or fewer customers.

P(X > 10) = 1 - P(X ≤ 10)

This will give us the probability of there being a significant delay at the drive-up window due to more than 10 customers arriving.

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48%

912 of 1900 can be written as:

912

1900

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

912

1900

×

100

100

= (

912 × 100

1900

) ×

1

100

=

48

100

Therefore, the answer is 48%

If you are using a calculator, simply enter 912÷1900×100 which will give you 48 as the answer.

Answer: 912 is what percent of 1900, the percent is 48%

The coordinates of the vertex B' are (-20, 0).

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Based on the information provided about triangle ABC, we have the following translation:

(x, y)                                              →                  (x - 3, y + 2)

Point B (-2, -2)                              →                  (-2 - 3, -2 + 2) = point B (-5, 0)

Next, we would dilate point B by a scale factor of 4 about the origin:

point B (-5, 0) →    (-5 × 4, 0 × 4) = point B' (-20, 0).

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In the diagram, if ΔABC= ΔDEF, then angle A is congruent to angle D.

Option C.

Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional in length.

Two triangles are considered similar if they satisfy one of the following conditions:

ABC ≅ DEF

∠A ≅ ∠ D

Thus, two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion, so angle A of triangle ABC is congruent to angle D of triangle DEF.

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Answer:

The table is the incorrect representation.

When we draw small and large samples from the same population, small samples produce a more peaked and narrower distribution.

This phenomenon is due to the presence of fewer degrees of freedom associated with the small samples. Variations between sample and population mean result in fewer degrees of freedom, which results in a greater variation between samples and the population mean.

Degrees of freedom (df) is a statistical measure that quantifies the number of values in the final calculation of a statistic that are free to vary. When we sample data from a population, we calculate the sample mean, standard deviation, and other statistics

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The value of x = -1 and y = -2 by solving the system of equation by using the substitution are 9x - y + 7 = 0 and 13x - 4y + 5 = 0

Given that,

The system of equation are 9x - y + 7 = 0 and 13x - 4y + 5 = 0

We have to solve the system of equation by using the substitution method.

We know that,

Take the system of equation

9x - y + 7 = 0 --------->equation(1)

13x - 4y + 5 = 0  ---------> equation(2)

From the equation (1)
9x - y + 7 = 0

y = 9x + 7

Substitute y = 9x + 7 in equation(2)

13x - 4y + 5 = 0

13x - 4(9x + 7) + 5 = 0

13x - 36x - 28 + 5 = 0

- 23x - 23 = 0

-23x = 23

x = -1

Now, Substitute x = -1 in equation(1)
y = 9(-1) + 7

y = -9 + 7

y = -2

Therefore, The value of x=-1 and y=-2

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The coordinates of the other endpoint of the segment, given the midpoint (4, 3) and one endpoint (10, 8), are (-2, -2).

To find the coordinates of the other endpoint of a segment given its midpoint and one endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

In this case, we are given the midpoint as (4, 3) and one endpoint as (10, 8). Let's assume the coordinates of the other endpoint are (x, y).

Using the midpoint formula, we can set up the following equations:

((10 + x)/2, (8 + y)/2) = (4, 3)

From the first equation, we can solve for x:

(10 + x)/2 = 4

10 + x = 8

x = 8 - 10

x = -2

From the second equation, we can solve for y:

(8 + y)/2 = 3

8 + y = 6

y = 6 - 8

y = -2

Therefore, the coordinates of the other endpoint are (-2, -2).

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Answer:

6x + 9 + 13x - 95 = 180

19x - 86 = 180

19x = 266

x = 14

z = 6(14) + 9 = 84 + 9 = 93

The function's y-intercept is 4, and the equation of its asymptote is y = 0. The graph shows that the function increases by a factor of [tex]\frac{3}{2}[/tex] each time x increases by 1. This function can be represented by the equation [tex]y = 4(\frac{3}{2})^x[/tex].

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the graph, we would calculate the value of a and b as follows;

[tex]f(x) = a(b)^x[/tex]

4 = a(b)⁰

a = 4

Next, we would determine value of b as follows;

6 = 4(b)¹

6 = 4b

b = 6/4

b = 3/2

Therefore, the required exponential function is given by;

[tex]y = 4(\frac{3}{2})^x[/tex]

In conclusion, the graph shows that the exponential function increases by a factor of [tex]\frac{3}{2}[/tex] or 1.5 each time x increases by 1.

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The freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.

To find the freezing point of a solution, we can use the formula:

ΔTf = Kf · m

where ΔTf is the change in freezing point, Kf is the freezing point depression constant (for water, Kf = 1.86 °C/m), and m is the molality of the solution (in moles of solute per kilogram of solvent).

First, we need to calculate the molality of the solution:

m = moles of solute / mass of solvent (in kg)

We are given that the solution is 0.33 m, which means there are 0.33 moles of Na₂SO₃ per kilogram of water. The molar mass of Na₂SO is:

2 Na + 1 S + 3 O = 2(23.0 g/mol) + 32.1 g/mol + 3(16.0 g/mol) = 126.0 g/mol

So, 0.33 moles of Na₂SO₃ is equal to:

0.33 mol × 126.0 g/mol = 41.6 g

Since we have 1 kg of water, the mass of the solvent is 1000 g. Therefore, the molality of the solution is:

m = 41.6 g / 1000 g = 0.0416 mol/kg

Now, ΔTf = Kf · m = (1.86 °C/m) · (0.0416 mol/kg) = 0.077 °C

freezing point = 0 °C - ΔTf = 0 °C - 0.077 °C = -0.077 °C

Therefore, the freezing point of a 0.33 m aqueous solution of Na₂SO₃ is -0.077 °C.

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Answer: -1.84

Step-by-step explanation:

3x1.86x0.33=1.84

0.00-1.84= -1.84

late answer but hope it helps someone!

The mean length of the words that are given above in a line plot would be = 4

The total number of words that where selected form the book = 15

The number of letters in each word is represented above in a line plot such as follows;

words with one letter = 3 ×1 = 3 letters

words with two letters = 2×2 = 4

Words with 3 letters = 1×3 = 3

words with four letters =4×4 = 16

words with six letters = 2 × 6 = 12

words with seven letters = 2×7 = 14

Words with eight letters = 1×8 = 8

Total word length = 3+4+3+16+12+14+8 = 60

But mean = total of given data/number of data

= 60/15

= 4

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8000 pounds is equal to 4 tons.

A pound is a unit of weight that is approximately equal to 16 ounces, while a ton is a unit of weight equal to 2000 pounds.

Therefore, to convert pounds to tons, you divide the weight in pounds by 2000.

8000 pounds is the weight that we want to convert to tons.

Dividing 8000 by 2000 gives us 4

which means that 8000 pounds is equal to 4 tons.

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To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.

       To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.

For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:

$11.34 / 14 = $0.81 per juice box

For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:

$12.64 / 16 = $0.79 per juice box

Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).

Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.

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To determine which option is the better buy between packs of 14 juice boxes for $11.34 and packs of 16 juice boxes for $12.64, we need to compare the cost per juice box for each option. The better buy is the one that offers a lower cost per juice box.

      To calculate the cost per juice box for each option, we divide the total cost of the pack by the number of juice boxes in the pack.

For the pack of 14 juice boxes priced at $11.34, the cost per juice box is:

$11.34 / 14 = $0.81 per juice box

For the pack of 16 juice boxes priced at $12.64, the cost per juice box is:

$12.64 / 16 = $0.79 per juice box

Comparing the two options, we find that the pack of 16 juice boxes offers a lower cost per juice box ($0.79) compared to the pack of 14 juice boxes ($0.81).

Therefore, the better buy is the pack of 16 juice boxes for $12.64, as it provides a lower cost per juice box.

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The proof that shows that sides SP is congruent to side TR is explained below.

First, using the given information, we have to establish that both triangles are congruent to each other, then state that the two sides are congruent since corresponding parts of congruent triangles are congruent.

Therefore, the correct proof is:

Statement                                 Reason                                            

1. QP ≅ QR; SQ ≅ TQ              1. Given

2. <SQP ≅ <TQR                     2. Vertical Angle Theorem

3. ΔSQP ≅ ΔTQR                    3. SAS congruence theorem

4. SP ≅ TR                               4. Corresponding parts of congruent              

                                                      triangles are congruent.

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The mean distance that the heavy ball was thrown in feet is 4.65 feet. This value tells us that on average, a typical throw of the ball results in a distance of 4.65 feet.

To find the mean, we need to first list all the distances and then find the sum of the distances. Finally, we will divide the sum by the number of distances.
Distances: 2.0, 2.2, 2.5, 3.1, 3.3, 3.4, 4.1, 4.1, 4.5, 5.0, 5.6, 6.7
Sum of distances: 2.0 + 2.2 + 2.5 + 3.1 + 3.3 + 3.4 + 4.1 + 4.1 + 4.5 + 5.0 + 5.6 + 6.7 = 51.5
Number of distances: 12
Mean = Sum of distances / Number of distances
Mean = 51.5 / 12 = 4.29 (rounded to two decimal places)
The closest answer to our calculated mean is:
4.65 feet; The value means that a typical throw of the ball results in 4.65 feet.

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The vector perpendicular to a plane determined by two vectors A and B can be found by taking their cross product. The unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.

A x B = (-2i+4j+0k) x (i+j-k)
= (-4k + 2i + 6j)

To find a unit vector perpendicular to the plane, we need to normalize this vector by dividing it by its magnitude:

|A x B| = sqrt((-4)^2 + 2^2 + 6^2) = sqrt(56)

So, a unit vector perpendicular to the plane determined by A and B is:

(-4k + 2i + 6j) / sqrt(56)

which simplifies to:

(-2i + 3j - k) / sqrt(14)

Therefore, the answer is (-2i + 3j - k).

To find a vector perpendicular to the plane determined by vectors A and B, you need to calculate the cross product of A and B.

A = -2i + 4j
B = i + j - k

Step 1: Calculate the cross product (C) of vectors A and B:
C = (A_y * B_z - A_z * B_y)i - (A_x * B_z - A_z * B_x)j + (A_x * B_y - A_y * B_x)k

Step 2: Plug in the values of A and B:
C = (4 * (-1) - 0 * 1)i - (-2 * (-1) - 0 * 1)j + (-2 * 1 - 4 * 1)k

Step 3: Simplify the expression:
C = -4i + 2j - 6k

Step 4: Find the magnitude of C:
|C| = √((-4)^2 + 2^2 + (-6)^2) = √(16 + 4 + 36) = √56

Step 5: Divide each component of C by its magnitude to find the unit vector:
Unit vector = (-4/√56)i + (2/√56)j + (-6/√56)k

So, the unit vector perpendicular to the plane determined by the vectors A and B is (-4/√56)i + (2/√56)j + (-6/√56)k.

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Answer: 12 different ways.

Step-by-step explanation:

For a set of M elements, the number of combinations of N elements (N ≤ M) is given by:

In this case, we know that there is a room that can hold two of the girls, then the number of combinations of the two girls that can be in that room is:

So these are the different combinations for the larger room.

So we assume that two girls already have a room, then we have two girls left and two rooms left.

For the first room, there are two possible girls that can be in, let's choose one of them.

For the last room, we have only one girl left, so we have one option.

The total number of combinations will be equal to the product between the number of options for each event (where the events are assigning the girls to the rooms)

Then the number of different outcomes is:

C = 6*2*1 = 12

There are 12 different ways.

Answer:

Step-by-step explanation:

[tex]\frac{325000}{550000} \\= \frac{325}{550} \\= \frac{65}{110}\\ = \frac{13}{22}[/tex]

Answer:

x-intercepts: (-4,0)

y-intercepts: (0,16)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

have a great day and thx for your inquiry :)

The equation of the parabola graphed below is given as follows:

x = -1/49(y - 2)² - 1.

The parabola in the context of this problem is in horizontal form, hence the equation is given as follows:

x = a(y - k)² + h.

In which the parameters are given as follows:

The coordinates of the vertex are given as follows:

(-1, 2).

Hence:

x = a(y - 2)² - 1.

When x = -2, y = -5, hence the leading coefficient a is obtained as follows:

-2 = a(49) - 1

a = -1/49.

Hence the equation is:

x = -1/49(y - 2)² - 1.

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If there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis.

To run stats testing on sales data from two different Buffalo Wild Wings stores, we need to use a correlation analysis. Specifically, we need to use Pearson's correlation coefficient to determine if there is a relationship between the number of employees and customer satisfaction. The Pearson's correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation and +1 indicating a perfect positive correlation. If the coefficient is close to zero, it indicates that there is no correlation.
The data we need to collect includes the number of employees in each store and the sales data for a specific period. We also need to gather customer satisfaction data, which can be collected through surveys or other feedback mechanisms. Once we have the data, we can use a statistical software program like SPSS or Excel to perform the correlation analysis.
If the correlation coefficient is positive and statistically significant, it means that there is a relationship between the number of employees and customer satisfaction. This could mean that more employees lead to better customer service, which in turn leads to higher customer satisfaction and sales. However, if the correlation is negative or not statistically significant, it means that there is no relationship between the two variables.
In conclusion, to determine if there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis. Gathering accurate data and using statistical software will allow us to determine if there is a significant relationship between the variables.

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Answer:

B=$18900.00

Step-by-step explanation:

B=?

P=9000

r=5%=0.05

t=2

B=p(1+r)t

B=9000×(1+0.05)×2

B=9000×(1.05)×2

B=9000×2.1

B=18900

Answer:

9

Step-by-step explanation:

This situation creates 3 similar triangles, so the lengths of corresponding sides are proportional.

1/3 = 3/x

x = 3 × 3

x = 9