lincoln high wants to estimate the number of seniors who plan to go to a 4-year college. answer the following.

The number of groups of three that the college can select is 56.

Total number of students = 8

Number of assistantships available = 3

Groups of three can be selected by the college means that out of the eight students three need to be selected at random and this can be done in ⁸[tex]C_{3}[/tex] ways.

In this case, we use combination and not permutation because the order of selection of the students does not matter.

Now, we know

ⁿ[tex]C_{r}[/tex] = ( n! )/( r! (n-r )!)

Here, n = 8 and r = 3

⁸[tex]C_{3}[/tex]  = ( 8! )/( 3! (8-3)! )

⁸[tex]C_{3}[/tex]  =  ( 8 × 7 × 6 × 5! )/ ( 3 × 2 × 1 × ( 5! ) )

⁸[tex]C_{3}[/tex]  = ( 8 × 7 × 6 )/ ( 3 × 2 )

⁸[tex]C_{3}[/tex]  = 56

The number of groups of three that the college can select is 56.

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Answer:

  x = 4

Step-by-step explanation:

You want the equation of the vertical line through (4, 6).

Slope is the ratio of rise to run for a line. When the "run" is zero, that ratio becomes undefined. The "run" will be zero for any rise when the line is vertical.

The equation of such a line has the form ...

  x = c . . . . . for some constant c

In order for this equation to be satisfied when (x, y) = (4, 6), the value of the constant must match the x-coordinate of the point.

The equation is x = 4.

Square root of Two is an irrational number. because we are unable to express it in the form a/b, where a and b are whole numbers and b is not zero.

Any real number that cannot be written as the quotient of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, the square root of 2 cannot be represented by an integer or a fraction.

Because these numbers may be represented on a number line, they are real numbers rather than complex numbers.

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three digits hope this helped

The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.

Let total number of bags = x

Let total number of apples Sharon has = y

If she packs 6 apples in each bag, she will have 3 apples left. So, mathematically we can write

6x + 3 = y                                                       equation 1

If she packs 7 apples in a bag, she will be four apples short. So, mathematically we can write

7x - 4 = y                                                         equation 2                

On subtracting equation 1 from equation 2 , we get

x - 7 = 0

⇒ x = 7

Substitute x = 7 in equation 1 , we get

6 ( 7 ) + 3 = y

⇒ y = 45

The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.

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We get that the number of pots that can be filled are 20 pots.

We are given that:

The total amount of yoghurt with Geela = 20 liters.

The amount of yoghurt in 1 pot = 1 liter

Now, we need to find the number of pots that can be filled.

So, we will do this by using division.

We get that:

Number of pots that can be filled. = 20 / 1

Number of pots that can be filled. = 20 pots

Therefore, we get that the number of pots that can be filled are 20 pots.

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Answer:

thsnk

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

3(5+5) = 30

3(10) = 30

<3

Answer:

1. 13 As there are 13 points indicating there are 13 students 2. 39.

Step-by-step explanation:

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &11\\ P=\textit{initial amount}\dotfill &160\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &14 \end{cases} \\\\\\ 11=160\left( \frac{1}{2} \right)^{\frac{t}{14}}\implies \cfrac{11}{160}=\left( \cfrac{1}{2} \right)^{\frac{t}{14}}\implies \log\left( \cfrac{11}{160} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{t}{14}} \right][/tex]

[tex]\log\left( \cfrac{11}{160} \right)=\cfrac{t}{14}\log\left[ \left( \cfrac{1}{2} \right)\right]\implies \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)}=\cfrac{t}{14} \\\\\\ 14\left( \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)} \right)=t\implies {\LARGE \begin{array}{llll} \stackrel{mins}{54.1}\approx t \end{array}}[/tex]

Answer: 2,8865 million acres of cropland in florida

Step-by-step explanation: To solve this problem we can multiply Alabama's cropland of 2.51 million acres by 1.15 giving: 2.51 million ×1.15=2.8865 million acres of cropland in Florida.

I Hope this helps :)

Answer: Florida has 2.8865 million acres of cropland.

Step-by-step explanation:

We can first do the multiplication, 2.51 x 1.15, and then add 1,255 + 2,510 + 25,100 then we get the answer: 2.8865

Answer:

P=6

Because 6/3=2

And 2+9=11

Step-by-step explanation:

Missy rode her bicycle 16 miles in 1 1 4 hours. Her average speed in miles per hour is 12.8 mph

Calculating average speed involves dividing the whole distance traveled by the total time it takes to cover that distance.

Speed is the rate of movement of anything at a specific time. Average speed refers to the average speed during the course of a journey. Typically, average speed refers to the speed of moving objects like cars, trains, and aircraft. It is frequently expressed in kilometers per hour (kph) or miles per hour (mph) (kph).

In many different disciplines, such as physics, astronomy, and transportation, average speed is employed.

As we know,

average speed is distance traveled divided by time taken

⇒ average speed = 16 miles × 5/4

⇒ average speed = 12.8 miles/hour

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Based on the calculations, the length, in cm, of an adjacent side of this rectangle is equal to 6.0 centimeters.

Given the following data:

Perimeter of rectangle = 40.0 centimeters.

Length of rectangle = 14.0 centimeters.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Note: The length of an adjacent side refers to the the width of this rectangle.

Substituting the parameters into the formula, we have;

40.0 = 2(14.0 + W)

40.0 = 28.0 + 2W

2W = 40.0 - 28.0

2W = 12.0

W = 12.0/2

Width, W = 6.0 centimeters.

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Answer:

A

Step-by-step explanation:

assuming you meant y = x² + 12x - 7 , then

given a quadratic in standard form

y = ax² + bx + c (a ≠ 0 )

the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 12x - 7 ← is in standard form

with a = 1 , b = 12 , then x- coordinate of vertex is

x = - [tex]\frac{12}{2}[/tex] = - 6

substitute x = - 6 into the equation for corresponding y- coordinate

y = (- 6)² + 12(- 6) - 7

  = 36 - 72 - 7

 = - 43

vertex = (- 6, - 43 )

Answer: The m<A = 55

Step-by-step explanation:

1. We know that m<A is likely congruent to m<B (know that m< means measure of angle) {Also noting congruent means same}

2. With that, we can tell that the given info is telling us that 124 is the total degree for m<D.

3. So, this tells us that 2x + x + 41.5 = 124 is the formula we will use.
       3a. 3x + 41.5 = 124 (Simplify)
               3b. 3x = 82.5 (Combine like Terms)
                         3c. x = 27.5 (Divide)

4. Now we know what x is, so finding m<A is easy, 2(27.5) equals to 55, meaning m<A is 55. For m<B, 27.5 + 41.5 equals to 69. To make sure 55 + 69 equals to 124

5. So:
m<A = 55
m<B = 69
m<D = 124

According to the given data The value of p is[tex]0.0351<0.1[/tex](alpha) so reject H₀

A left-tailed test is used when the alternative hypothesis claims that the true value of the parameter suggested by the null hypothesis is lower than the null hypothesis implies. If the sample being tested is within the one-sided critical zone, the alternative hypothesis will be accepted rather than the null hypothesis.

Financial analysts employ the one-tailed test to confirm an investment or portfolio hypothesis.

If our statistical analysis finds that the significance level is smaller than the set cut-off value, we reject the null hypothesis and accept the alternative hypothesis (for example, either 0.05 or 0.01).

z = -1.81alpha

= 0.1p [tex]( z < -1.81 )p ( z < -1.81 )[/tex]

= 0.0351 ( from z table )P &lt;

alpha, reject H₀

When the p-value is less than or equal to alpha, hypothesis H0 is rejected;

however,

if the p-value is greater than alpha, hypothesis H0 is not rejected.

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Answer:

Step-by-step explanation:

Using similar triangles, it is found that the measure of angle B is of 74º.

Similar triangles are triangles that have the same angle measures, and whose side lengths are proportional.

In this problem, the triangle ABC was translated, resulting in triangle A'B'C'. A translation does not change the measures of the angles, hence their angles are given as follows:

80º, 26º and B.

The sum of the internal angles of a triangle is of 180º, hence:

80 + 26 + B = 180

B = 74º.

The measure of angle B is of 74º.

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Answer:

A

Step-by-step explanation:

x² + 7x + 12 = 0

consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)

the factors are + 3 and + 4 , since

3 × 4 = + 12 and 3 + 4 = + 7 , then

(x + 3)(x + 4) = 0

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 4 = 0 ⇒ x = - 4

Answer:

1080

Step-by-step explanation:

Answer:

97th term of arthmetic progression is

-16+ 96* 18

Step-by-step explanation:

The total amount that Mikaela spent on the paddleboard is $514.16

The given parameters are:

Original cost = $799

Discount = 40%

State tax = 7.25%

The total amount that Mikaela spent on the paddleboard is calculated as

Amount = Original cost * (1 - Discount) * (1 + State tax)

This gives

Amount = 799 * (1 - 40%) * (1 + 7.25%)

Evaluate

Amount = 514.16

Hence, the total amount that Mikaela spent on the paddleboard is $514.16

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Answer:

(B)  $514.16

Step-by-step explanation:

Correct on my quiz.

The number of overtime hours done by electrician, as found by unitary method, is 4.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given:

To find: Number of Overtime hours

FInding:

Let the number of overtime hours be 'x'.

By unitary method, Charge of 1 regular hour = $24

Charge of 8 regular hours = $24(8) = $192

Again, by unitary method, Charge of 1 overtime hour = $36

Charge of x overtime hours = $36(x)

Cost of Materials = $202

Now, total bill = sum of all the expenses

=> 538 = 192 + 36x + 202

=> 538 - 294 = 36x

=> 144 = 36x

=> 4 = x

Hence, the number of overtime hours as found by unitary method is 4.

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The expressions of all the functions are;

1) f(x) = 0.75x

2)g(x) = 0.8x

3) (f o g)(x) = 0.6x

4) (g o f)(x) = 0.6x

We are told that f(x) is the price with the $20 coupon applied, and

g(x) is the price with the 15% discount applied. Thus;

1) An expression for f(x) is;

f(x) = (1 - 0.25)x = 0.75x

f(x) = 0.75x

2) An expression for g(x) is;

g(x) = (1 - 0.2)x = 0.8x

g(x) = 0.8x

3) An expression for (f o g)(x) is;

(f o g)(x)  = f(g(x)) = 0.75(0.8x) = 0.6x

(f o g)(x) = 0.6x

4) An expression for (g o f)(x) is;

(g o f)(x) = 0.8(0.75x) = 0.6x

(g o f)(x) = 0.6x

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16 times larger is the new area when compared to the original.

Given that, the length of each side of the square is quadrupled.

We need to find how many times larger is the new area when compared to the original.

A square is a closed two-dimensional shape with four equal sides and four equal angles. The four sides of the square form the four angles at the vertices. The sum of the total length of the sides of a square is its perimeter, and the total space occupied by the shape is the area of the square. The formula to calculate the area of a square is a².

Let the length of each side of the square be x.

Then the length of each side of the new square will be 4x.

Now, the area of the original square = x²

The area of the new square = (4x)² = 16x²

So, the new square = 16 × the original square

Therefore, 16 times larger is the new area when compared to the original.

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Using a linear function, it will take 8 years for the Springfield zoo to have 35 gorillas.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the parameters are given as follows:

m = 4, b = 3.

Hence the number of gorillas after x years is given by:

G(x) = 3 + 4x.

It will have 35 gorillas when:

G(x) = 35.

Hence:

3 + 4x = 35.

4x = 32.

x = 32/4

x = 8.

It will take 8 years for the Springfield zoo to have 35 gorillas.

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Answer:

Step-by-step explanation:

To find y = f(g(x)) replace the x in f(x) by g(x):-

y = 4^(x - 3)

---> y = 4^x  * 4^-3

---> y = (4)^x / 64

Answer:

-21 degrees

Step-by-step explanation:

-14 - 7 = 21

Answer: 5859375

Step-by-step explanation:

3, 15, 75...

75/15=5

15/3=5

Every term multiplied by 5 is the next term. Hence, the equation for this sequence can be expressed as:

y=3*[tex]5^{x-1}[/tex]    ==> y is the term when x is the term number and 3 is the first number in the sequence

Now let's solve for the 10th term:

y=3*[tex]5^{10-1}[/tex]

y=3*[tex]5^{9}[/tex]

y=3*1953125

y=5859375

Answer:

Hope this helps :)

21) 31 + 14

22) 16 - 9

23) 7 + 4 + 18

24) 3 × 40

25)

26) 81 ÷ 3 OR 81/3 (the fraction bar also means divide)

27) 3 × 2 = 6

28) 7 x 6 = 42 (7 days in a week times by 6 weeks equal 42 days)