A highly selective university will only admit students who place at least 2-zcores above the mean on the ACT that
has a mean of 18 and a standard deviation of 6. What is the minimum score that an applicant must obtain to be
admitted to the university?

259.25π in² is the surface area of the cone

The surface area of a cone can be calculated using the formula SA = πr² + πrl

where r is the radius and l is the slant height.

Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.

The slant height (l) is given as 22 inches.

Substituting these values into the formula:

Surface Area = π(8.5)² + π(8.5)(22)

= 72.25π + 187π

= 259.25π

Therefore, the surface area of the cone is 259.25π in²

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Answer:

B. 4x² - 20x  + 26

Step-by-step explanation:

→Set it up, like so:

(2x - 5)² + 1

4x² - 20x + 25 + 1

→Add like terms (25 and 1):

4x² - 20x + 26

Answer:

70

Step-by-step explanation:

700 / 10 = 70

Answer:

70

Step-by-step explanation:

700 ÷ 10 = 70

Answer:

the sum will be negative

The sum will always be negative because the positive number would have to be larger than the negative for the outcome to be positive.

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Step-by-step explanation:

Whenever you have brackets, you have to multiply the outside with all of the insides.

6 + 4x(3+4) = 6 + [ (4x×3) + (4x×4) ]

= 6 + [ 12x + 16x ]

= 6 + 28x

Answer: 6+28x

Answer:

1. 5.2

2. 5.7

3. 5.1

4. 5.425 or 5.4

Step-by-step explanation:

hope this helps :)

Answer:

1. 5.2

2. 5.7

3. 5.1

4. 5.4

Step-by-step explanation:

you can use the app photo math, you just take a picture of the problem and it will give you the answer and explain the steps.

Answer:

Wait...

Step-by-step explanation:

Step-by-step explanation:

0.75a + 2(0.90) = 27.60

is the correct answer

Answer:

A) Yes, because the sum of any two side lengths is greater than the third side length.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 4 + 8 = 12, which is greater than 10, and the other two combinations (4 + 10 and 8 + 10) also satisfy this rule. Therefore, the given side lengths do form a triangle.

Step-by-step explanation:

Step-by-step explanation:

remember, y = f(x)

so, the question is really for what x is y = 1 ?

and what is the y-value for x = -1 ?

a)

when we imagine a horizontal line through y = 1, at what points (x-value) does this line cross the function graph ?

as we can see, at x = -2 and x = 2.

pick one for your answer.

b)

now we imagine a vertical line through x = -1.

at what point (y-value) does this line cross the function graph ?

as we can see, at y = 4.

f(-1) = 4

Answer:

17x and (5x+2) + (7x+ 3)

Step-by-step explanation:

Miguel finished the 36 km in 1 hour and 30 minutes.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

18 km = 1 hour

9 km = 30 minutes

Now,

Total distance = 36 km

Distance done by Miguel = 9 kilometers

So,

The distance remaining.

= 36 - 9

= 27

Now,

Time taken to run 27 km.

18 km = 1 hour

Multiply 27/18 on both sides.

27 km = 27/18 x 1 hour

27 km = 1.5 hour

Thus,

1 hour and 30 minutes.

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Complete question.

Right now, Miguel is 9 kilometers into a 36-kilometer race. He is running an average of 18 kilometers every hour.

After how many hours Miguel will finish the 36 km.

Answer:

Step-by-step explanation:

The diagrammatic expression to understand this question very well is attached in the image below.

By applying the law of cosine rule; we have:

From the diagram attached below, we need to determine the side "b" by using equation (2) from above:

b² = a² + c² - 2ac Cos B

From the information given:

a = 12 miles;  c = 18 miles;   ∠B = 38°

∴

replacing the values into the above equation:

b² = 12² + 18² - 2(12)(18) Cos (38°)

b² = 144 + 324 - 432 × (0.7880)

b² = 468 - 340.416

b² = 127.584

\(b = \sqrt{127.584}\)

b = 11.30 miles

However, we are also being told that the speed from A → C = 6.8 mph

Thus, the time required to go from A → C  can be determined by using the relation:

\(\mathbf{speed = \dfrac{distance}{time}}\)

making time the subject of the formula, we have:

\(\mathbf{time= \dfrac{distance}{speed }}\)

\(\mathbf{time= \dfrac{11.30}{6.8}}\)

time = 1.66 hours

By using the paved roads, the speed is given as = 22 mph

thus, the total distance covered = |AB| + |BC|

= (18+12) miles

= 30 miles

∴

\(\mathbf{time= \dfrac{distance}{speed }}\)

\(\mathbf{time= \dfrac{30}{22}}\)

time = 1.36 hours

Therefore, the time used off-road = 1.661 hours while the time used on the paved road is 1.36 hours.

Since we are considering the shortest time possible;

We can conclude that it would be faster for the bicyclist to ride from A to C on the paved roads since it takes a shorter time to reach its destination compared to the time used off-road.

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It would be faster for the bicyclist to ride from A to C on the paved roads since the time to go from A to C on the paved roads is 1.4 h and the time to go from A to C off-road is 1.7 h.        

To calculate which way would be faster we need to find the distance from point A to C with the law of cosines:

\( \overline{AC}^{2} = \overline{AB}^{2} + \overline{BC}^{2} - 2\overline{AB}\overline{BC}cos(38) \)

Where:

\(\overline{AB}\): is the distance between the point A and B = 18 mi

\(\overline{BC}\): is the distance between the point B and C = 12 mi        

\( \overline{AC} = \sqrt{(18 mi)^{2} + (12 mi)^{2} - 2*18 mi*12 mi*cos(38)} = 11.3 mi \)

Now, let's find the time for the two following cases.

1. From point A to C on the paved roads (t₁)

\( t_{1} = t_{AB} + t_{BC} \)

The time can be calculated with the following equation:

\( t = \frac{d}{v} \)    (1)

Where:

d: is the distance

v: is the velocity

Then, the total time that it takes the bicyclist to go from point A to C on the paved roads is:

\( t_{1} = t_{AB} + t_{BC} = \frac{18 mi}{22 mph} + \frac{12 mi}{22 mph} = 1.4 h = 84 min \)

2. From point A to C off-road (t₂)

With equation (1) we can calculate the time to go from point A to C off-road:

\( t_{2} = \frac{\overline{AC}}{v_{2}} = \frac{11.3 mi}{6.8 mph} = 1.7 h = 102 min \)

Therefore, it would be faster for the bicyclist to ride from A to C on the paved roads.  

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Answer:

16

Step-by-step explanation:

mode = the most

mean = ave

median = the no. in between

so arrange those five costs the one in the middle is 16

Answer:

length: 601 1/3 area: 361601 7/9

Step-by-step explanation:

the maximum area would be a square, and we only need 3 sides, so we can divide the amount of fencing by 3

1804/3=601 1/3

the length is 601.(3)

square to find the area

(1804/3)^2

361601 7/9

area is 361601 7/9

Answer:

1. 7

2. 48

Step-by-step explanation:

you have to subtract 49-42 because some got taken away then you should end up with 7, 63-15 is 48.

p chart from this data are attached below.

Describe about p chart?

P bar = total detective / total sampled

P bar = \(\frac{20}{100}\)

         = \(\frac{1}{5}\)

UCL = P bar + L . \(\sqrt{\frac{p bar q bar}{n} }\)

        = \(\frac{1}{5}\) + 3 * \(\sqrt{\frac{1}{5} *\frac{4}{5} * \frac{1}{100} }\)

        = (\(\frac{1}{5} + \frac{3 * 2}{50}\))

        = (0.20 + 0.12)

UCL = 0.32

CL = P bar = 0.20

LCL = P bar - L . \(\sqrt{\frac{p bar q bar}{n} }\)

       = (\(\frac{1}{5} - \frac{3 * 2}{50}\))

       = (0.20 - 0.12)

LCL  = 0.08

Therefore, UCL = 0.32, CL =  0.20, LCL  = 0.08

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There are 20 students have more than 2 pets.

We have to given that;

A line plot titled Number of Pets of Third Grade Students.

Here, By given information we get;

Number of students have more than 2 pets are,

⇒ 4 + 2 + 3 + 0 + 1 + 5 + 1 + 1 + 3

⇒ 20

Thus, There are 20 students have more than 2 pets.

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The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

First, we need to compute the volume of the rectangular prism, as follows:

x⁴ - 8x² + 17 is the function that represents the fog(x).

To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):

g(f(x)) = g(x² - 4)

Now, we can substitute the expression for g(x) into the above expression:

g(f(x)) = (x² - 4)² + 1

Expanding the squared term, we get:

g(f(x)) = x⁴ - 8x² + 17

Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.

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Complete question:

f(x) = x² - 4 and g(x)= x^2 + 1  find fog(x).

Answer:

Step-by-step explanation:

\(-5\frac{1}{7} \div 2\frac{2}{5} =-\frac{36}{7}\div \frac{12}{5}\)

                \(=-\frac{36}{7} \times \frac{5}{12}\)

                \(=-\frac{3}{7} \times \frac{5}{1}\)           (÷ top and bottom by 12)

                \(=-\frac{15}{7}\)

                \(=-2\frac{1}{7}\)

Answer:

3. a. 10:35= 2:7

b.35:45=7:9

c.40:50=4:5

x = 2 is the solution of the given equation: x + 3x - 4 = 10 - 3x

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

x + 3x - 4 = 10 - 3x

or, 4x - 4 = 10 - 3x

or, 4x + 3x = 10 + 4

or, 7x = 14

or, x = 14/7

or, x = 2

Thus, x = 2 is the solution of the given equation: x + 3x - 4 = 10 - 3x

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