Q6) Solve the following LPP graphically: Maximize Z = 3x + 2y Subject To: 6x + 3y ≤ 24 3x + 6y≤ 30 x ≥ 0, y ≥0

A hypothesis test for two proportions is a statistical procedure used to determine if the proportions of two different groups are statistically different from each other.

A hypothesis test for two proportions is a statistical procedure used to determine if the proportions of two different groups are statistically different from each other. The first step is to determine the null hypothesis, which states that there is no difference between the proportions of the two groups. Then, the alternative hypothesis is formed, which states that there is a difference between the proportions of the two groups. The next step is to calculate the test statistic, which is typically a z-score or a t-score. This test statistic is then used to calculate the p-value, which is the probability of obtaining the observed result if the null hypothesis is true. If the p-value is less than the predetermined significance level, then the null hypothesis is rejected in favor of the alternative hypothesis and it can be concluded that there is a difference between the proportions of the two groups.

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Answer:

43.3 ft

Explanation:

The diagram representing this problem is drawn and attached below:

The distance between the boy and the tree = x

Recall from trigonometrical ratios:

Therefore:

The distance between the boy and the tree is 43.3 ft (correct to 2 decimal places).

Answer

12

Explanation

2xand 3x

let 3 be 3x

3x=18

X=18/3

X=6

now

2x=2multiply6

12

the number of boys is 12

Answer:

Step-by-step explanation:

Inverse variation equation:

We have:

Work out the value of k by substituting the values of x and y:

The equation is:

Answer:

y = -6/x

Step-by-step explanation:

y varies inversely as x

So, y = k/x, where k is the constant of proportionality.

If y = -1 when x = 6,

Then, -1 = k/6 ===> k = -6

Therefore, y = -6/x

Answer:

D

Step-by-step explanation:

Dustin's mean number of situps is 42.5714285714, while Jacob's is 41.4285714286.

You can get the mean of Dustin's data by adding all of the data of Dustin's situps together and dividing by 7, and the same thing with Jacob's.

The investor can obtain an annual annuity payment of approximately $48,651 for his retirement years.

To calculate the annual annuity payment, we can use the present value of an ordinary annuity formula. The formula is:

PV = C × [(1 - (1 + r)^-n) / r]

Where:

PV is the present value of the annuity,

C is the annual payment,

r is the interest rate,

n is the number of periods.

In this case, the investor has a retirement period of 25 years, and the interest rate is 7.5%.

The present value of the annuity is the amount the investor can invest today plus the present value of the annual payments he can make for 30 years.

Using the formula, we can solve for C, the annual payment, which comes out to approximately $48,651.

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Answer:

$.59 per apple

Step-by-step explanation:

The unit cost is the price divided by the number of items

3.54 / 6

.59

$.59 per apple

Answer:

0.59 or .59

Step-by-step explanation:

3.54 divided by 6

According to the question, srs is a simple random sample whose size consists of individuals from the population and chosen in such a way that every set of individuals has an equal chance to be sampled.

What is Stratified random samples?

For stratified random samples, initially classify the population into the groups of similar individuals which is called as “strata”. Later choose simple random samples and combine them to form a full sample.

As per question, srs of \(200\) of the \(25000\) undergraduate students and the srs of \(100\) of the \(500\) graduate students. This overall sample is a stratified sample.

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Answer:

n

Step-by-step explanation:

n

Answer:

18 students took the bus to school.

Step-by-step explanation:

If 1/4 of the students walked, that leaves 3/4 of the students who did not walk. That leaves 22.5 students. Out of these students 22.5, 4/5 of them take the bus, and 4/5 of 22.5 is 18.

The vertex of the function defined as g(x) = f(x) − 2 is (3, 3)

The definition of the quadratic function is given as

y = f(x)

Also, we have the vertex of the function f(x) to be

(3, 5)

The transformed function of f(x) is given as

g(x) = f(x) - 2

This means that

g(3) = f(3) - 2

Point (3, 5) implies that

f(3) = 5

So, we have

g(3) = 5 - 2

Evaluate

g(3) = 3

This means that the vertex of g(x) is (3. 3)

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In the given coordinate plane, based on the given dilation the line r has slope 8 and coordinate (0,8)

Dilation:

Dilation refers the ratio of the given line to line by the scale factor.

Given

In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 3 with center (0, 3).

Here we need to find the the slope and y-intercept of line r.

Here we know that scale factor is 3.

Let us consider the slope of the line r will not change and the intercept is the addition of their ordinate will be.

So, it can be written as,

=> Intercept = 5 + 3

=> Intercept = 8

Therefore, the line r has slope 8 and coordinate (0.8).

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Answer:

Step-by-step explanation:

H

Answer:

The best estimate for the value of the given expression is -2 1/2. Correct: Second alternative

Explanation:

Estimate and Number Rounding

There are situations where numbers must be estimated according to certain rules. If we have a number and we need a good approximate to it, we can use rounding to the required number of decimals.

The question requires to find the best estimate for the operation:

\(\displaystyle \left(\frac{34}{8}-\frac{16}{3}\right)-\frac{14}{9}\)

We calculate the decimal value of the expression:

\(\displaystyle \left(\frac{34}{8}-\frac{16}{3}\right)-\frac{14}{9}=(4.25-5.33)-1.56=-2.64\)

The first alternative is incorrect. It's a good approximation because it's close to the number, but the next alternative is the closest of all choices.

The second alternative Is correct. The value of -2 1/2 is -2.5. The number -2.64 is closer to -2.5 than to -3 which is the alternative A.

The third alternative Is incorrect. 7 is a positive number and it's not even close to -2.64

The last alternative Is incorrect. 7 1/2 = 7.5 is a positive number and it's not even close to -2.64

Answer:

x=1.5

Step-by-step explanation: 2 times 1 and 2 times 2 equals

4x-6=4x+6

6+6+12

8x=12

Answer:

1390 cm^3

Step-by-step explanation:

9 x 7 x 10 = 630 cm^3 for the rectang prism top

area * 10 for the bottom

8 x ( 12 + 7)/2   * 10 = 760 cm^3  for the trap base

total = 1390 cm^3

We have the surface equation to be 4x² + y² + z² = 10 and the tangent plane equation 2x + 3z = 10. Let us solve for z in terms of x:2x + 3z = 103z = 10 - 2xz = (10 - 2x) / 3We know that a point P(x, y, z) is on the surface and the tangent plane passes through P. Also, the gradient vector of the surface at P is perpendicular to the tangent plane, which means that the vector <8x, 2y, 2z> is perpendicular to the vector <2, 0, 3>.

Therefore, their  product equals zero:8x * 2 + 2y * 0 + 2z * 3 = 016x + 6z = 0 Substitute z with (10 - 2x) / 3:16x + 6(10 - 2x) / 3 = 0Simplify:16x + 20 - 4x = 0Solve for x:12x = - 20x = - 5 / 3Substitute x into z = (10 - 2x) / 3:z = (10 - 2(-5 / 3)) / 3z = 20 / 9The point P is (-5/3, y, 20/9), where y² + 4/9 + 400/81 = 10y² = 310/81 - 4/9 = 232/405y = ± √232 / 27√5P can be any of the two points P₁ = (-5/3, √232/27√5, 20/9) or P₂ = (-5/3, - √232/27√5, 20/9) on the surface 4x² + y² + z² = 10 such that 2x + 3z = 10 is an equation of the tangent plane to the surface at P.

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Answer:

x*$9.00 + y*$11.00 ≥ $120

x + y ≤ 20 hrs

Step-by-step explanation:

we have the variables:

x = hours she spends dog-walking

y = hours she spends washing cars.

We know that she wins $9.00 per hour of dog-waling, and she wins $11.00 per hour of washing cars, then the total amount of money she wins per hour is:

x*$9.00 + y*$11.00

And she needs to earn at least $120, then we have the inequality:

x*$9.00 + y*$11.00 ≥ $120

And we also know that she can work, at most, 20 hours per week, then:

x + y ≤ 20 hrs

Then the system of inequalities that represents this situation is:

x*$9.00 + y*$11.00 ≥ $120

x + y ≤ 20 hrs

Answer:

\(615.44\ in^2\)

Step-by-step explanation:

The equation for the area of a circle is:

\(A=\pi r^2\)

Please note that "A" stands for "Area" and "r" stands for "radius".

We can substitute the given values into the equation:

\(A=\pi r^2\\A=3.14*14^2\\A=3.14*196\\A=615.44\ in^2\)

Answer:

sinθ-cosθ = 0

sinθ= cosθ

sinθ/cosθ = 1

tanθ = 1

Bu tan45 = 1

So,

tanθ=tan45

θ = 45°

sin45 = 1/√2  cos45 = 1/√2

sin⁴θ+cos⁴θ  = (1/√2)⁴+(1/√2)⁴

                     = 1/4+1/4 = 2/4 = 1/2 = 0.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this helped you..................

The distance between the two cities on the map is 0.45 inches , the correct  option is (A) 0.45inches  .

In the question ,
it is given that

the scale factor of the  map is 25 miles = 0.1 inches

So, 1 mile = 0.1/25 inches

= 0.004 inches

So , on the map 1 mile is represented by 0.004 inches

Given that the real distance between the two cities is 112.5 miles

So , on the map  112.5 miles = 112.5*0.004 inches

= 0.45 inches

Therefore , the distance between the two cities on the map is 0.45 inches , the correct  option is (A)0.45inches  .

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Answer: the answer is 0.667 or 2/3 or 66%

The probability of scoring a goal exactly 8 times by Jon is given by 0.0234. It is obtained using the prerequisite knowledge of binomial distribution and probability.

What is Binomial Distribution in Probability?

When each trial has a probability of occurring equally likely, then the number of trials or observations is outlined using the binomial distribution. The chance of observing a specific number of successful outcomes in a specific number of trials is determined by using the binomial distribution.

Calculation of the probability of the given event

Total no. of possible outcomes, n = 11

The probability that Jon will kick the ball in the net, p(x) = 0.4

The probability that Alex will kick the ball in the net, q(x) = 0.6

Using Binomial Distribution, we get,

P(x = r) = C(n,r) × (p)r × q(n - r)

where x is the score made by Joe

P(x = 8) = C(11,8) × (0.4)8 × (0.6)3

             = 0.0234

Hence, the probability that Jon will score exactly 8 times is 0.0234.

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The 2 unknown numbers are 4 and 5 .

Let the numbers be x and x + 1.

From the given information,

\(\dashrightarrow\sf \ \ \ x^2 + (x + 1)^2 = 41 \\ \\ \\ \)

\(\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 = 41 \\ \\ \\ \)

\(\dashrightarrow\sf \ \ \ 2 {x}^{2} + 2x + 1 - 41=0 \\ \\ \\ \)

\(\dashrightarrow\sf \ \ \ {x}^{2} + x - 20 = 0 \\ \\ \\ \)

\(\dashrightarrow\sf \ \ \ (x + 5)(x - 4)=0 \\ \\ \\ \)

\(\dashrightarrow\sf \ \ \ { \underline{ \boxed{ \bf{ \red{x = - 5,4}}}}} \ \bigstar \\ \\ \)

But, as we know -5 is not a natural number,

Hence, x = 4 .

So the 2 unknown numbers are :

★ Solution :

Let the number be x and x + 1.

\(\rule{130}1\)

\(\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}\)

\(:\implies\sf x^2 + (x + 1)^2 = 41 \\\\\\:\implies\sf 2x^2 + 2x + 1 - 41 = 0\\\\\\:\implies\sf 2x^2 + 2x + 40 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + x - 20 = 0\\\\\\:\implies\sf x^2 + 5x - 4x - 20 = 0\\\\\\:\implies\sf x(x + 5) - 4(x + 5) = 0\\\\\\:\implies\sf (x + 5)(x - 4) = 0\\\\\\:\implies\underline{\boxed{\sf x = -5, 4}}\)

⠀

We know that -5 is not a natural number. Hence, x = 4.

\(\therefore\:\underline{\textsf{The two consecutive natural number is \textbf{4 and 5}}}.\)

Answer:

1. volume = 1243.44ft^3

2. volume = 54259.2ft^3

The direction and by how many units should f(x) be shifted to match g(x) is Left by 6 units. Option C

To determine the direction and magnitude of the shift needed for f(x) to match g(x), we can compare the corresponding values of f(x) and g(x) in the table.

For x = -2, f(x) = 4 and g(x) = 64.

For x = -1, f(x) = 1 and g(x) = 49.

For x = 0, f(x) = 0 and g(x) = 36.

For x = 1, f(x) = 2 and g(x) = 25.

For x = 2, f(x) = 4 and g(x) = 16.

By comparing the values, we can observe that the graph of f(x) is shifted to the right compared to g(x). To match the graph of g(x), we need to shift f(x) to the left.

The magnitude of the shift can be determined by the difference in x-values between the corresponding points of f(x) and g(x).

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The value of x and y in the line segment are 6 and 6.5 units repsectively.

The lines are three parallel lines cut by two transversal lines. The transversal lines that cut across the parallel lines have same length at intervals .

Using the information in the diagram let's find the value of x and y in the diagram.

Therefore,

2x + 1 = x + 7

2x - x = 7 - 1

x = 6 units

Therefore,

3y - 8 = y + 5

3y - y = 5 + 8

2y = 13

divide both sides by 2

y = 13 / 2

y = 6.5 units

Therefore,

x = 6 units

y = 6.5 units

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