Name the rule for each statement: (SSS, ASA, SAS, AAS) Hint: you may use some of the rules more than once. Two triangles are congruent if: a) each pair of corresponding sides is congruent b) two pairs of corresponding angles are congruent and a pair of corresponding sides are congruent c) two pairs of corresponding sides and the angles included between them are congruent d) If three sides of one triangle are congruent to three sides of a second triangle, e) If two angles and a non-included sides of each triangle are congruent

The value of y, when x = 2 1/3 in a direct variation scenario where y = kx (k being the constant of variation), is approximately 233.3.

In the given problem, the value of y varies directly with x. This means there's a constant of variation, k, such that y = kx. We can find k by plugging in the initial given values, x=1/4 and y=25, into this equation, which gives us k = y/x = 25/(1/4) = 100.

Now that we know k, we can calculate the value of y when x = 2 1/3 using the same equation. Here, y = kx = 100 * 2 1/3 = 100 * 7/3 = 700/3 = 233.3 recurring.

So, when x = 2 1/3, y is approximately 233.3.

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When [tex]\(x = \frac{1}{4}\), \(y = 25\)[/tex] in a direct variation relationship. The constant of variation[tex](\(k\))[/tex] is found to be 100. Thus, when[tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]

If the value of [tex]\(y\)[/tex]  varies directly with[tex]\(x\),[/tex]  we can express this relationship using the formula [tex]\(y = kx\),[/tex]  where [tex]\(k\)[/tex] is the constant of variation.

Given that when [tex]\(x = \frac{1}{4}\), \(y = 25\),[/tex]  we can use this information to find [tex]\(k\)[/tex]:

[tex]\[25 = k \times \frac{1}{4}\][/tex]

Solving for [tex]\(k\):[/tex]

[tex]\[k = 25 \times 4 = 100\][/tex]

Now that we know [tex]\(k = 100\),[/tex]  we can find the value of[tex]\(y\)[/tex]  when[tex]\(x = 2 \frac{1}{3}\)\\[/tex]

[tex]\[y = 100 \times 2 \frac{1}{3} = 100 \times \frac{7}{3} = \frac{700}{3}\][/tex]

Therefore, when [tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]

Answer:

The larger pizza is less expensive per square inch

Step-by-step explanation:

we know that

The area of a circle (pizza) is equal to

[tex]A=\pi r^{2}[/tex]

step 1

Find the area of the smaller pizza

we have

[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=(3.14)(5)^{2}=78.5\ in^{2}[/tex]

Find the price per square unit

Remember that

The price of one smaller pizza is [tex]\$15/2=\$7.5[/tex]

so

[tex]\frac{7.5}{78.5}\frac{\$}{in^{2}}=0.10\frac{\$}{in^{2}}[/tex]

step 2

Find the area of the larger pizza

we have

[tex]r=16/2=8\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=(3.14)(8)^{2}=200.96\ in^{2}[/tex]

Find the price per square unit

so

[tex]\frac{17}{200.96}\frac{\$}{in^{2}}=0.08\frac{\$}{in^{2}}[/tex]

Therefore

The larger pizza is less expensive per square inch

Answer:

The object first reaches 72 feet after 1.5 seconds; it is this height again after 2.5 seconds.

Step-by-step explanation:

To find the amount of time it takes to reach 72 feet, we solve the equation

72 = -16t² + 64t + 12

To solve this, we will set it equal to 0 by subtracting 72 from each side:

72-72 = -16t² + 64t + 12 - 72

0 = -16t² + 64t - 60

Next we will use the quadratic formula to solve this:

By setting up and solving the required quadratic equation, it is determined that an object propelled from a height of 12 feet with an initial velocity of 64 feet per second will take 3.75 seconds to reach a height of 72 feet.

The height h of the object is given by the equation h = -16t^2 + 64t + 12. We need to solve for time t, where the height h is 72 feet. By setting the equation equal to 72, we get 72 = -16t^2 + 64t + 12.

Moving -16t^2 and 64t to the other side, we get 16t^2 - 64t + (72 - 12) = 0. This simplifies to 16t^2 - 64t + 60 = 0. Divide every term in the equation by four to get: 4t^2 - 16t + 15 = 0. This equation must now be solved using the quadratic formula: t = [-b +/- sqrt(b^2 - 4ac)] / (2a).

Plugging in the values a=4, b=-16, and c=15, we get two possible solutions: t = 1 and t = 3.75 seconds. As the object is propelled up and comes down, we take the larger value, t=3.75 seconds, because that's the actual duration for the object to reach the height of 72 feet.

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the answer is -3 because i searched it and that’s what came up

The answer is -3 hope this helps

Answer:

Should be the first one again

The dotted line is a vertical line at x -2, so we know the first equation is X<-2

The solid line means the equation has to be less  than or equal to and since it crosses the dotted line at -2

the second equation would be y <=-x-2

The first choice is correct.

Answer:

your 3rd option because 3^3 is 27

I agree because when you do prime factorization you get 27 by doing it

Answer:maybe A.

but I'm not sure

Answer:

C.) 6

Step-by-step explanation:

x-6 = -6

Inververse Operation

-6=+6

(Honestly don't know if that is the right reasons but that is what I have been doing and I have got those answers right so maybe I'm doing it right...)

Answer:

the first answer is A y^2=8x

Step-by-step explanation:

The equation of a parabola that opens to the right with vertex at the origin (0,0) and has a focal width of 8 is y^2 = 8x. This follows from the equation of a parabola in standard form, y^2 = 4ax, where 4a equals the focal width.

The equation of a parabola in standard form is either y^2=4ax or x^2=4ay, depending on its orientation. The vertex is at the origin (0,0). A parabola that opens to the right or left has the form y^2 = 4ax, and one that opens upward or downward has the form x^2 = 4ay. Given that your parabola opens to the right and has a focal width of 8, it would utilize the first form. The focal width is the absolute value of 4a. Thus, for your parabola, 4a is equal to the focal width, which is 8. Therefore, a = 8/4 = 2. Hence, the equation of the parabola with vertex at the origin that opens to the right and has a focal width of 8 is y^2 = 8x.

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Answer:

In London it cost $ 6.017 while in Newyork it cost $2.831

so NewYork is cheaper

Step-by-step explanation:

As we know, 1 US gallon = 3.785 liters

so,converting liters into gallon = 1.089 * 3.785

                                                   = 4.121 per gallon

Cost of 4.121 gallon petrol in dollars = 4.121 * 1.46

                                                            = $ 6.017

In London it cost $ 6.017 while in Newyork it cost $2.831

so NewYork is cheaper

Final answer:

Petrol is better value for money in New York, where it costs approximately £0.512 per litre after converting from USD to GBP and gallons to litres, compared to £1.089 per litre in London.

Explanation:

To determine where petrol is better value for money, we need to compare the cost per litre in both London and New York, taking into account the exchange rate and units of measure. First, let's convert the cost of petrol in New York from gallons to litres:

Now, let's compare it to the cost in London:

Comparing the two:

Therefore, the petrol is better value for money in New York as £0.512 per litre is less than £1.089 per litre.

Answer:

After 7 years it will have a value of $13.946 to the nearest dollar.

Step-by-step explanation:

As it depreciates by 8% (0.08) a year the value of the car after each year is

1 - 0.08 = 0.92 of the previous year's value.

So we have the formula:

Value =  25,000(0.92)^7

= $13,946.17 (answer).

Answer:

The rounded answer is equal to 14000

Step-by-step explanation:

Answer: last option (5π√146 units²)

Step-by-step explanation:

To solve the exercise you must apply the formula for calculate the lateral area of a cone, which is shown below:

 [tex]LA=r*L*\pi[/tex]

where r is the radius but L is the slant height.

As you can see in the figure attached:

[tex]r=5[/tex]

But you need to find the slant height with the Pythagorean Theorem (L would be the hypotenuse):

[tex]L=\sqrt{11^2+5^2}=\sqrt{146}[/tex]

Substitute into the formula, then:

 [tex]LA=(5)(\sqrt{146})\pi=5\pi\ \sqrt{146[/tex]units²

Answer:

The correct answer is 5√146π  square units

Step-by-step explanation:

From the figure we can see a cone

Points to remember

Lateral surface area of cone = πrl

r - Radius of cone

l - Slant height of cone

To find the slant height

From figure we get,

r = 5 units and height = 11 units

Slant height² = radius² + height² =  5² + 11² = 25 + 121 = 146

Slant height = √146 units

To find the lateral area

lateral area = πrl =  π * 5 * √146  = 5√146π  square units

The correct answer is 5√146π  square units

Answer:

  Not an exponential function. The exponent is a constant.

Step-by-step explanation:

An exponential function has the variable in the exponent. This function raises the variable to a fixed power, so it is not an exponential function.

➷ Congruent means it is the same shape and size. Therefore, A is incorrect as a triangle and a square aren't the same shape. The same applies to B. C is also incorrect as not all circles are the same size.

In short, the correct answer is option D. None of the above is true.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

The answer is B

Step-by-step explanation:

Congruent means In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Meaning a square and an rectangle are congruent because they both have four sides

Plus: I just took the test and got it right

Answer:   b. 3

Step-by-step explanation:

The limit of the function as it approaches -3 from the left is 3.

The limit of the function as it approaches -3 from the right is 3.

Since the limit from the left equals limit from the right, then the limit of the function exists and is 3.

Answer: 3, or b

Step-by-step explanation:

The rule that it comes from both the right and the left and meets at a common point verifies this.

To find the measure of angle z, subtract the measures of angles x and y from 180°. Therefore, angle z = 180° - 30° - 35° = 115°.

The subject of the question is geometry, specifically dealing with the measures of angles. Without more context, it's difficult to provide an exact answer. However, if angles x, y, and z form a triangle, then the measure of angle z can be found using the property that the sum of all angles in a triangle is 180°.

To find the measure of angle z, you need to recall that the sum of the angles in a triangle is always 180°. So, you can start by finding the measure of angle z by subtracting the measures of angles x and y from 180°.

Therefore, angle z = 180° - 30° - 35° = 115°.

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Answer:

$18.30

Step-by-step explanation:

First, you can figure out the cost per golf ball by dividing the price by the number of golf balls. If 6 balls = 7.32, then 1 ball = 7.32/6, or 1.22. Now you can multiply this by the number of balls in the box to find out the price: 1.22 * 15 = 18.30.

Another way to solve this is to set up a ratio of balls / price:

(x is the unknown price)

[tex]\frac{6}{7.32} =\frac{15}{x}[/tex]

Now, cross-multiplying, you find that 6x = 7.32 * 15, or 6x = 109.8. Dividing both sides by 6, you get x=18.30.

Answer:

BC = 8

Step-by-step explanation:

These are similar shapes, so they multiply out to the same ratio.

Seeing that 10 * 1.5 = 15, BC * 1.5 should equal 12.

All we do is divide 1.5 from both sides to get 8.

Then, plug it back into the equation to check and it works.

Answer:  x = 8

Step-by-step explanation:

You can solve by setting up the proportions of the corresponding sides of the pentagon and then solve for x (the value of BC).  

So, IJ/DE values are 15/10 and are set equal to GH/x (x represents the value of BC; the value you are solving for).  Hint: It may be helpful for you to draw a diagram of the two pentagons and label them with the letters and values provided in the problem.  This will help you to set up your proportion problem accurately.

To solve you can cross multiply to find the value of x.

15/10 = 12/x

15x = 12 * 10

15x = 120

x = 120/15

x = 8

I think the number of ways is 671?

Answer: 151.1

Step-by-step explanation:

First, you would add all the heights together (153+150+151+152=606)

Then you would divide 606 by the number of numbers in the data set in this case the number of family members which is (606 divided by 4= 151.1)

Answer:

151.5

Step-by-step explanation:

First of all, what is the mean in a set of numbers?

To find the average of these numbers, we'll add all of the numbers and divide it by 4, the number of actual terms, in the set.

(153 + 150 + 151 + 152) / 4 = 151.5

Answer:

Step-by-step explanation:

XYZ

The first one

I hope I helped you.

Dylan earns $17.50 per hour for 4 hours, yielding a total income of $70. After deducting 15% of his total earnings ($10.50) for income taxes, Dylan's earnings reduce to $59.50.

To answer this question, we first need to calculate Dylan's total earnings before taxes. He earned $17.50 per hour for 4 hours, so his total earnings would be 4 hours * $17.50/hour = $70.

Next, we determine the amount of income tax. Dylan's income tax rate is 15%, so he would pay 15% of his total earnings in taxes: 15/100 * $70 = $10.50 in taxes.

Finally, we calculate Dylan's net earnings after tax by subtracting the tax amount from his total earnings: $70 - $10.50 = $59.50. Therefore, Dylan will earn $59.50 after taxes for 4 hours of work.

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Dylan earns $59.50 after taxes.

To calculate the amount Dylan earns after taxes, we need to first find out his total earnings before taxes.

Dylan works for 4 hours and is paid $17.50 per hour, so his total earnings before taxes are 4 hours multiplied by $17.50, which is $70.

Next, we need to calculate the amount of income tax Dylan needs to pay. He must pay 15% of his total earnings as income taxes, which is 15% of $70, which is $10.50.

To find out how much Dylan earns after taxes, we subtract the income tax amount from his total earnings,

so $70 - $10.50 = $59.50.

Therefore, Dylan earns $59.50 after taxes.

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Answer:

a: no the sample size is too small

b:  Yes, the distribution is normal with a mean of 40 and standard deviation of 12

Step-by-step explanation:

a:  If n < 30, we need to know that the sample is normally distributed or else we can't determine anything.  When sample sized get very large, they usually resemble normally distributed data sets so we can still make conjectures even if the data isn't officially normally distributed

b: The question tells us that the sample is normally distributed, so even though n < 30, we can still make conjectures about the population

Answer:

23

Step-by-step explanation:

angles in a triangle add up to 180 so

124+33=157

180-157=23

x=23

y is 23 as well and z is 124

To find the values of f(g(0)), g(f(2)), and g(g(0)), substitute the given values into the functions step-by-step.

1.) To find the value of f(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function f(x): f(2) =  rac{2-2}{3} = 0.

2.) To find the value of g(f(2)), we first substitute 2 into the function f(x): f(2) =  rac{2-2}{3} = 0. Then, substitute the value obtained into the function g(x): g(0) = 3(0) + 2 = 2.

3.) To find the value of g(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function g(x) again: g(2) = 3(2) + 2 = 8.

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To find the value of f(g(0)), substitute 0 into g(x) to get g(0) = 2 and then substitute this value into f(x) to get f(g(0)) = 4/3. To find the value of g(f(2)), substitute 2 into f(x) to get f(2) = 4/3 and then substitute this value into g(x) to get g(f(2)) = 8. To find the value of g(g(0)), calculate g(0) = 2 and then substitute this value into g(x) to get g(g(0)) = 8.

To find the value of f(g(0)), we need to substitute the value of 0 into the function g(x) to get g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function f(x) to get f(2) = 2 - 2/3 = 4/3.

To find the value of g(f(2)), we need to substitute the value of 2 into the function f(x) to get f(2) = 2 - 2/3 = 4/3. Then, we substitute this value into the function g(x) to get g(4/3) = 3(4/3) + 2 = 6 + 2 = 8.

To find the value of g(g(0)), we need to calculate g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function g(x) again to get g(2) = 3(2) + 2 = 8.

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Answer:

For the shape of the distribution of the sample proportion to be approximately​ normal, it is required that ​np (1 -p ) greater than or equals 10.

Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals​0.35.

Step-by-step explanation:

Normal distribution is the shape data takes as a symmetrical bell shaped curve. Normal approximation can only be taken when np or np(1-p) greater than 10.

Fill in the blanks to complete the following statements:

The first blank should be filled with '5' as per the npq rule for approximation using normal distribution and the second statement's blank is filled with '0.35', which is the population proportion.

To complete your statements:

It's essential to remember that in hypothesis testing of a single population proportion, the binomial distribution's shape needs to be similar to a normal distribution. The terms 'np' and 'nq' refer to the conditions for this binomial distribution. Here 'n' is the number of trials, 'p' is the probability of success, and 'q=1-p' is the probability of failure, both must be more significant than five for the approximation to be acceptable.

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Answer:

i think its 912

Step-by-step explanation:

i am not sure though

The sum of the first 19 terms of the given arithmetic series is equal to 912.

Given the following sequence:

A arithmetic series can be defined as a series of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

Mathematically, an arithmetic series is given by the expression:

[tex]S_n = \frac{n}{2}(2a +(n-1)d)[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]S_{19} = \frac{19}{2}(2(3) +(19-1)5)\\\\S_{19} = 9.5(6+18(5))\\\\S_{19} = 9.5(6+90)\\\\S_{19} = 9.5 \times 96[/tex]

19 term = 912.

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1/9 has to be divided by 5 if it is shared by others.

1/9 divided by 5 is 1/45 and each person would have 1/45

Answer is 1/45

Answer:

1:  z = 1.96

2:  t = 2.552

Step-by-step explanation:

1:  When you don't know the population standard deviation and the sample size is large, you can still use a z test because many large samples are relatively normally distributed.  A 95% confidence interval uses a z-score of 1.96

2.  We are told that n < 30, so we use t distribution.  Use the degrees of freedom, which is one less than the population, and the column that has 0.02 in the area of 2 tails.

In constructing a confidence interval, if the standard deviation is unknown and the population appears skewed, we typically use the t-distribution. However, without enough information given, the answer to the first problem tends towards 'Neither normal nor t distribution applies'. For the second problem, the standard deviation is given and the population appears normally distributed, hence answer is 'zα/2 = 2.33' from the z-table.

The relevant subject matter here is Statistics, specifically, confidence intervals. The construction of a confidence interval depends on the knowledge of the standard deviation and whether the population is normally distributed or not.

For the first problem, since the standard deviation (σ) is unknown and the population appears to be skewed, student's t-distribution applies here. This would involve using tα/2 with degree of freedom (n-1) in place of the unavailable standard deviation. However, without enough data provided in the question, it is difficult to correctly compute tα/2. The answer therefore likely tends towards option E: 'Neither the normal nor the t distribution applies'.

For the second problem, the standard deviation (σ) is given and the population appears to be normally distributed. This suggests the normal distribution applies, hence you would compute zα/2, the critical value for the z-score at a 98% confidence level. Referring to a standard z-table at a 98% confidence level gives a z-score of approximately 2.33. So, the answer for this scenario is A: zα/2 = 2.33.

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Answer:

6%

Step-by-step explanation:

120/2000= 60/1000= 6/100= 6%

6% of the  money was spent on keyboard

percentage, a relative value indicating hundredth parts of any quantity.

Given that school principal spent $2,000 to buy some new computer equipment.

Out of $2000 , $120 was used to buy some new keyboards

We need to find  what percent of the money was spent on keyboard.

We need to find what is $120 of $2000

Let x/100 is the percent of amount spent for keyboard

x/100×2000=120

20x=120

Divide both sides by 20

x=6

Hence, 6% of the  money was spent on keyboard

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Answer:

v/4

Step-by-step explanation:

Volume of cylinder a = v

Let the height of cylinder a is h and its radius is r. The volume of cylinder a will be:

[tex]v=\pi r^{2}h[/tex]

Height of cylinder b is same as cylinder a. So height of cylinder b is h.

Radius of cylinder b is half of radius(width) of cylinder a. So radius of cylinder b will be r/2

The volume of cylinder b will be:

[tex]v^{'}=\pi (\frac{r}{2} )^{2}h\\\\ v^{'}=\pi(\frac{r^{2}}{4})h \\\\ v^{'}=\frac{\pi r^{2}h}{4} \\\\ v^{'} = \frac{v}{4}[/tex]

Thus the volume of cylinder b will be v/4

Answer:

The volume of cylinder A is four times the volume of cylinder B.

Step-by-step explanation:

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