Match each system of equations to its point of intersection.
y = x + 3
y=-3x - 2
y = -x - 7
y=x+3
y = -x - 7
y = 2x + 1
y = 2x + 1
y=-3x - 2
5
4
y = 2x + 1
y = x3
2
5
3
2
-1
2
3
4
-2
-4
ntum All rights reserved

Answer:

x = 4.2

Step-by-step explanation:

8x - 14 = 2x + 11 (Given)

8x = 2x + 25 (Addition)

6x = 25 (subtraction)

x = 4.16666666667 (division) which is about

x = 4.2 (rounding to nearest tenth)

A. Translation

This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance. When you are doing a translation, the primary object is called the pre-image, and the object after the translation is called the image.

B. Rotation

This type of transformation has an object about a fixed point without changing its size or shape.

C. Reflection

A reflection is a transformation that reflects each point in the preimage across a line of reflection. It is a rigid motion so it preserves length and angle measure

A perpendicular bisector is a line (ray, segment) which cuts a line segment into two equal parts at90° angle

D. A transformation is a change in the position or size of an object Movements that do not change the size or shape of the object moved are called “rigid transformations” There are three types of rigid transformations: Translations, Reflections, and Rotations. These are more commonly referred to as Slides, Flips, and Turns.

The p-value associated with the null hypothesis = 0.05

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours

Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.

You have the Hypothesis that "students study less than 10 hours, on average, per week"

Symbolically:

H₀:μ≥10hours

H₁:μ<10hours

The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.

The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.

Therefore,

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

The p-value associated with the null hypothesis = 0.05

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The valuation of the notes in a years is given as follows:

y = 200(0.00000006)^a.

The yearly inflation rate is of:

1,666,666,667%

The valuation changed by a percentage in a period of time, hence an exponential function is used to model the situation.

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

The initial valuation is of $200, hence the parameter a is given as follows:

a = 200.

Thus the function should be modeled as follows:

\(y = 200(b)^a\)

In which a is the time in years.

In one month, the amount decayed to $50. One month is 1/12 of a year, as one year is composed by 12 months, hence the parameter b is obtained as follows:

\(50 = 200(b)^{\frac{1}{12}}\)

\((b)^{\frac{1}{12}} = \frac{50}{200}\)

\((b)^{\frac{1}{12}} = \frac{1}{4}\)

Elevating both sides to 12, we have that:

b = (0.25)^12

b = 0.00000006.

Hence the function is:

y = 200(0.00000006)^a.

The inflation rate is given as follows:

1/0.00000006 x 100% = 1,666,666,667%

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Answer:

The football team is on their own 11-yd line.

Step-by-step explanation:

The team starts at 15, and then goes back 7, and the advances 3 yards.

The equation to model this is:

\(15-7+3=11\)

Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.

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The number of stamps given for the books in question are :

To find the number of stamps needed for 1 book, the formula is :

= Stamps needed for 19 books / Number of books

= 380 / 19

= 20 stamps

For 7 books :

= 7 books x 20 stamps per book

= 140 stamps

For 12 books :

= 12 books x 20 stamps per book

= 240 stamps

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During the record-breaking run, the cheetah was traveling at an approximate speed of 37.282 miles per hour.

To calculate the cheetah's speed in miles per hour, we need to convert the distance and time from meters and seconds to miles and hours, respectively.

1 mile is equal to approximately 1609.34 meters, and 1 hour is equal to 3600 seconds.

Distance in miles:

100 meters = 100 / 1609.34 miles

Time in hours:

5.95 seconds = 5.95 / 3600 hours

Now, we can calculate the speed in miles per hour by dividing the distance (in miles) by the time (in hours):

Speed = (100 / 1609.34) / (5.95 / 3600) miles per hour

Simplifying the expression:

Speed ≈ (100 * 3600) / (1609.34 * 5.95) miles per hour

Calculating the approximate value:

Speed ≈ 37.282 miles per hour

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Rolle's Theorem states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), and if f(a) = f(b), then there exists at least one point c in (a,b) where f'(c) = 0.

In this case, the given function is f(x) = -2x² - 12x + 7 over the interval [-6,0]. To find all values of c in this interval where f'(x) = 0, we first need to find the derivative of f(x):

f'(x) = -4x - 12

Now, we need to solve for x when f'(x) = 0:

-4x - 12 = 0
-4x = 12
x = -3

Therefore, the only value of c in the interval [-6,0] where f'(x) = 0 is -3.

Answer: c = -3.  

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Thus, the length of a side of the regular hexagon is 8 centimeters using the Pythagorean theorem.

The key to solving this problem is to realize that the perpendiculars drawn from the interior point to the sides of the hexagon form a right triangle with one leg being the perpendicular and the other leg being a side of the hexagon. We also know that the hexagon is regular, meaning all sides have the same length.

Let's label the length of the side of the hexagon as "x". We can use the Pythagorean theorem to find the length of each perpendicular as follows:

- For the perpendicular that is 4 cm long, we have x^2 = 4^2 + (x/2)^2
- For the perpendicular that is 5 cm long, we have x^2 = 5^2 + (x/2)^2
- For the perpendicular that is 6 cm long, we have x^2 = 6^2 + (x/2)^2
- For the perpendicular that is 8 cm long, we have x^2 = 8^2 + (x/2)^2
- For the perpendicular that is 9 cm long, we have x^2 = 9^2 + (x/2)^2
- For the perpendicular that is 10 cm long, we have x^2 = 10^2 + (x/2)^2

Simplifying each equation and using a bit of algebra, we get:

- 3x^2 = 16^2
- 7x^2 = 25^2
- 12x^2 = 36^2
- 24x^2 = 64^2
- 33x^2 = 81^2
- 40x^2 = 100^2

Solving for x in each equation, we find that x = 8 cm. Therefore, the length of a side of the regular hexagon is 8 centimeters.

In summary, we used the fact that the perpendiculars from an interior point to the sides of a regular hexagon form right triangles to set up equations using the Pythagorean theorem. Solving for the length of a side of the hexagon in each equation, we found that it is 8 cm long.

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Answer:

C)

Step-by-step explanation:

the number of mailboxes and the number of teachers in a city represents association with no causation. Association refers to a relationship between two variables, where one variable may be related to the other in some way. However, causation refers to a relationship where one variable causes the other to occur. In this case, the number of mailboxes in a city is not causing the number of teachers in the city to change, nor is the number of teachers causing the number of mailboxes to change. Therefore, there is an association between the two variables, but no causation.

The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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The Perimeter of the Figure is 42 inch.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

Given:

The measurement 10in, 7 in, 9 in and 11 in

So, the Perimeter of the Figure

= 10 + 11 + 3 + 9 + 7 + 2

= 42 inch

Hence, the Perimeter is 42 inch

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Answer:

x=1/2 I'm not sure it may be wrong

Answer:

The question to the question provided is

\( \frac{1}{2} \)

The Chi-square test of variance is appropriate to use.

The correct model from the list to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units by sampling the GPAs of 40 SJSU students is the "One sample, Chi-square test of variance. "The Chi-square test of variance is used to determine whether the variance of a population is equal to a specific value. In the Chi-square test of variance, the null hypothesis is that the variance of the population is equal to the specific value or the variance is not greater than the specific value. The Chi-square test of variance is used when the sample is random, the sample is normally distributed, and the variable is measured on a continuous scale. In the given problem, the researcher wants to support the hypothesis that the standard deviation of semester units taken by SJSU students is over 4 semester units.

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The wire stretches by approximately 0.0132 meters when a weight of 5.2 kN is hung from it.

The amount of stretch in the wire can be found using the formula:

ΔL = (F x L) / (A x E)

where ΔL is the amount of stretch, F is the force applied, L is the original length of the wire, A is the cross-sectional area of the wire, and E is the Young's modulus of the material.

Substituting the given values, we get:

ΔL = (5.2 x 10³ x 2.2) / (4.9 x 10\(^-6\) x 9.2 x 10\(^10\))

ΔL ≈ 0.0132 meters

Therefore, the wire stretches by approximately 0.0132 meters when a weight of 5.2 kN is hung from it.

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(a) The complete Venn diagram is in the image attatched.

(b) The probability that a number chosen from the universal set is a member of A ∩ B is  1/15 = 6.67 %.

The complete Venn diagram is calculated by applying the following formula.

The given elements of the set include the follow;

U = {odd numbers less than  30}

A = {9, 15, 17, 19 }

B = {5, 15, 25}

C = {9, 15, 21, 27}

The elements of A intercept B, A intercept C and B intercept C is ;

A ∩ B = {15}

A ∩ C = {9, 15}

B ∩ C = { 15}

A ∩ B ∩ C = { 15 }

(b) The probability that a number chosen from the universal set is a member of A ∩ B.

total number of samples in the universal set = {29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1}

= 15

P (A ∩ B) = 1/15 = 6.67 %

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Answer:

Step-by-step explanation:

Answer:

Answer:

y = 4x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 3 when y = 12

k =  =  = 4

y = 4x ← equation of variation

Step-by-step explanation:

The main difference between Save and Save As is that Save helps to update the lastly preserved file with the latest content while Save As helps to store a new file or to store an existing file to a new location with the same name or a different name.mark me brainlist if i help

Answer:

difference between save and save as is that save helps to update lastly preserved file with least content while save as to store a new file or to store an existing file to a new location with the same name or different name.

We need to identifying whether or not if this is a function

So, we will apply the vertical line test , we will graph a vertical line

If the vertical intersects withe the given graph at more than one point , so, the graph will not be a function

show the following image :

as shown : the vertical line at x = -6 intersects with the graph at two points

So, The graph is not a function

So, the answer is No

​

Answer:

576

Step-by-step explanation:

450 x 0.04 (0.04 meaning 4%) is 18, then 18 x 7 by the number of years listed, thats 126, then 450 + 126 = 576, by 7 years it would be worth 576, went up by 28%.

Laura's net proceeds were -$94.43. This means that she lost $94.43 on the transaction.

What is the commission?

A commission is a fee or percentage of a sale that is paid to a person or organization for their services in facilitating or completing a transaction. Commissions are commonly used in sales or business settings, where an individual or organization acts as a middleman between a buyer and a seller.

Laura's total cost for buying the stock was:

55 shares x $3.50/share = $192.50

Her broker's commission was 1% of $192.50, which is:

$192.50 x 0.01 = $1.93

So, her total cost including commission was:

$192.50 + $1.93 = $194.43

Her total revenue from selling the stock was:

55 shares x $2/share = $110

Her broker's fee for selling the stock was $10.

So, her total cost for selling the stock was:

$10

Therefore, Laura's net proceeds were:

$110 - $194.43 - $10 = -$94.43

This means that Laura lost money on the transaction.

Hence, Laura's net proceeds were -$94.43. This means that she lost $94.43 on the transaction.

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On average, approximately 3.152 customers will be waiting in the queue at the stadium.

To calculate the average number of customers waiting in the queue, we can use the queuing theory formulas. The arrival rate of customers is given as 180 per minute, which means the arrival rate is λ = 180/60 = 3 customers per second. The service time is given as an average of 21 seconds per customer, so the service rate is μ = 1/21 customers per second.

To calculate the utilization factor (ρ), we divide the arrival rate by the service rate: ρ = λ/μ. In this case, ρ = 3/1/21 = 9.857.

Next, we calculate the coefficient of variation for arrival time (C_a) and service time (C_s) using the given values. C_a = 13% = 0.13 and C_s = 13% = 0.13.

Using the queuing theory formula for the average number of customers waiting in the queue (L_q), we have L_q = ρ^2 / (1 - ρ) * \((C_{a}^2 + C_{s}^2)\) / 2.

Plugging in the values, L_q = \((9.857^2) / (1 - 9.857) * (0.13^2 + 0.13^2) / 2 = 3.152\).

Therefore, on average, approximately 3.152 customers will be waiting in the queue at the stadium.

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Answer:

x = 1/12

Step-by-step explanation:

2/3x + 1/4 = (8x+3) /12   (create equivalent fractions with a denominator of 12)

23/3x - 1/3 = (23x - 1) /3            *(46/6x = 23/3x)

8x + 3  =  23x - 1

    12            3

now cross-multiply:

3(8x + 3) = 12(23x - 1)

24x + 9 = 273x - 12

9 = 252x - 12

21 = 252x

x = 21/252 which reduces to 1/12

The quadratic formula to find the roots:l = (60 ± √(60² - 4(1)(800))) / (2(1))simplify:l = (60 ± √(3600 - 3200)) / 2l = (60 ± √400) / 2simplify:l = 30 ± 10l = 20 or l = 40The length of the garden can be between 20 ft and 40 ft.

The area of a rectangle is the product of the length and width of the rectangle. We can use the formula to write an equation in terms of the length of the rectangle given that the area of the rectangle must be at least 800 ft²:A = lw800 = lwmultiply both sides by w:800/w = lWe know that the gardener has 120 ft of deer-resistant fence.

The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. We can use the formula to write an equation in terms of the length of the rectangle given that the gardener has 120 ft of deer-resistant fence:P = 2l + 2w120 = 2l + 2wmultiply both sides by 1/2:60 = l + wsubtract l from both sides:60 - l = wWe want to find the range of possible values for the length of the garden

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The inverse of \(f^{-1}\) of the function f is inverse is swapping of coordinates x and y and making y as subject.

Inverse function is represented by  with regards to the original function  and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

Generally, the method of calculating an inverse is swapping of coordinates x and y. This newly created inverse is a relation but not necessarily a function. The original function has to be a one-to-one function to assure that its inverse will also be a function.

Therefore, the inverse of \(f^{-1}\) of the function f is inverse is swapping of coordinates x and y and making y as subject.

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Answer:

7/12

Step-by-step explanation:

10 white balls and 14 red balls = 24 balls

P( red) = number of red balls / total balls

           =14/24

           =7/12

The length of the diameter is 17.5

A diameter is a line segment that divides a circle into two equal parts.

The diameter is the line of symmetry of the circle and it divides the circle to form semi-circles.

The length of a line segment with end coordinates is calculated using the formula below,

D = \(\sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} -y_{1}) ^{2} }\)

Where, \(x_{2}\) = 6, \(x_{1}\) = -1,  \(y_{2}\) = 21,  \(y_{1}\) = -1

D = \(\sqrt{(6--1)^{2} + (21-5)^{2} }\)

D = \(\sqrt{(7)^{2} + (16)^{2} }\)

D = \(\sqrt{49 + 256}\)

D = \(\sqrt{305}\)

D = 17.5

In conclusion, the diameter of the line segment is 17.5

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