HELP ME PLEASE PLEASE

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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The number of pieces in the bowl before she added the 20 is 8 pieces of candy

Here, we want to get the number of pieces in the bowl before the addition of the 20 pieces

Let the number of pieces before the addition be n

she added 20 pieces to what is there initially, this brings the total to;

Now, two days after the addition, half of the above is gone

Half of the above is;

Now, the difference between the number of pieces in the bowl after the addition of the 20 and the half gone is 14; we have the equation as thus;

The proper method of solution for the question "By how many degrees did the temperature rise during the first 4 hours?" is to subtract the liquid's initial temperature from its temperature 4 hours later, which is option (C).

To find the change in temperature, we need to calculate the temperature difference between the initial and final temperatures of the liquid. Since we are asked about the temperature rise, we need to subtract the initial temperature from the temperature after 4 hours. This gives us the total increase in temperature. Option (A) is incorrect because it only gives the value of the rate of change of temperature at time 4, but not the temperature change over the entire 4 hour period. Option (B) is also incorrect, as it does not provide any information about the temperature at all. Option (D) is incorrect because dividing by 4 assumes that the temperature change is constant over the entire 4 hour period, which may not be true. Therefore, option (C) is the correct method of solution to find the number of degrees the temperature of the liquid rose during the first 4 hours.

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Answer:

The result is a right cone

Step-by-step explanation:

The factored expression of 3x^3y - 75xy is 3xy(x^2- 25)

The expression is given as:

3x^3y - 75xy

Factor out xy

3x^3y - 75xy = xy(3x^2- 75)

Factor out 3

3x^3y - 75xy = 3xy(x^2- 25)

Hence, the factored expression of 3x^3y - 75xy is 3xy(x^2- 25)

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In the given case, the required critical value is 2.485.

To find the critical value t* for a t-distribution with a sample size of 26 and a probability of 1% for values greater than t*, we need to consider the degrees of freedom (df) and the given tail probability.

In this case, the degrees of freedom (df) will be equal to the sample size minus 1, which is 26 - 1 = 25. The tail probability is given as 1%, which is equal to 0.01.

To find the critical value t*, you can use a t-distribution table or calculator. Look for the value at the intersection of the row with 25 degrees of freedom and the column corresponding to a tail probability of 0.01.  Using a t-distribution table or calculator, the critical value t* is approximately 2.485. Therefore, the required critical value is 2.485.

Note: The question is incomplete. The complete question probably is: What is the value of t*, the critical value of the t distribution for a sample of size 26, such that the probability of being greater than t* is 1%? The required critical value is ____________ .

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1/3

each cat gets 1/3 of the food because 2/3 ÷ 2/1 = 1/3.

True course = arctan((0 + 30 sin(240°)) / (190 + 30 cos(240°)))

To solve the problem, we can use vector addition to find the true course and ground speed of the plane.

First, let's break down the velocities into their components.

The airspeed of the plane is 170 mph at a heading of 135°. We can represent this velocity as V_plane = <170 cos(135°), 170 sin(135°)>.

The wind currents are running at 30 mph at an angle of 175° clockwise from due north. We can represent this velocity as V_wind = <30 cos(175°), 30 sin(175°)>.

To find the true course, we need to find the resultant velocity, which is the sum of the plane's velocity and the wind velocity.

V_resultant = V_plane + V_wind

Now, we can calculate the components of the resultant velocity:

V_resultant = <170 cos(135°) + 30 cos(175°), 170 sin(135°) + 30 sin(175°)>

To find the ground speed, we can calculate the magnitude of the resultant velocity:

Ground speed = |V_resultant| = sqrt((170 cos(135°) + 30 cos(175°))^2 + (170 sin(135°) + 30 sin(175°))^2)

Round the ground speed to the nearest ten.

Finally, to find the true course, we can calculate the angle of the resultant velocity using arctan:

True course = arctan((170 sin(135°) + 30 sin(175°)) / (170 cos(135°) + 30 cos(175°)))

Round the true course to the nearest whole number.

To find ∠C and a in triangle ABC, we can use the Law of Cosines.

The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, we have:

c^2 = a^2 + b^2 - 2ab cos(C)

Given ∠A = 25 degrees, ∠B = 110 degrees, and the area of triangle ABC is 80 square inches, we can find ∠C using the formula:

∠C = arccos((a^2 + b^2 - c^2) / (2ab))

Once we have ∠C, we can use the area formula for a triangle:

Area = (1/2) * ab * sin(C)

Substituting the given values, we can solve for a.

To find the true course of the plane, we need to consider the net velocity, which is the vector sum of the plane's airspeed and the wind velocity.

Given that the airspeed of the plane is 190 mph due east and the wind currents are moving at a constant speed in the direction 240 degrees clockwise from due north, we can break down the velocities into their components.

The airspeed of the plane is <190, 0> mph, and the wind velocity is <30 cos(240°), 30 sin(240°)> mph.

To find the net velocity, we add the two vectors:

Net velocity = <190 + 30 cos(240°), 0 + 30 sin(240°)> mph

The true course is the angle between the net velocity vector and the north direction, oriented clockwise.

To find the true course, we can use arctan:

True course = arctan((0 + 30 sin(240°)) / (190 + 30 cos(240°)))

Round the true course to the nearest whole number.

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Answer:

i think the surface would be 2

Answer:

Step-by-step explanation:

You want to know the values of k that make the line 4y = k(x +4) either parallel or perpendicular to the line 12y = 9x +8.

The slopes of parallel lines are the same. When the equation of a line is written in "y =" form, the slope is the coefficient of x. Here, the two equations written in that form are ...

For parallel lines, we want to choose the value of k so that the slopes are equal:

  k/4 = 3/4

  k = 3 . . . . . . . . multiply by 4

The slopes of perpendicular lines have a product of -1. This means we want to choose k so that ...

  (k/4)(3/4) = -1 . . . . . the product of slopes k/r and 3/4 is -1

  k = -16/3 . . . . . . . . . multiply by 16/3

__

Additional comment

The attached graph shows the original line (dashed red) and the parallel and perpendicular lines with their respective values of k.

Given:

The function is,

Replace x by -x in the given function,

It is observed that, when the x is replace by -x the function end up with exactly opposite of the given function.

Thus, the given function is odd.

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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The matrix is not invertible for any values of b and c.

We can determine if the matrix is invertible or not by checking if its row reduce echelon form (RREF) is the identity matrix. We can use elementary row operations to transform the matrix into its RREF without using determinants:

0 1 1 0 0 b  c  

0 0 b 1 0 c-b 0  

0 0 0 0 1 -c -b  

0 0 0 0 0 0  1

The first row of the matrix has a pivot in the second column, so we can use it to eliminate the entries below it. Next, we can use the third column to eliminate the entry in the second row, fourth column. Then, we can use the fifth column to eliminate the entry in the third row, sixth column. Finally, we have a row of zeros in the fourth row, which means that the rank of the matrix is less than 3, so it cannot be invertible.

Therefore, the matrix is not invertible for any values of b and c.

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The 53586077 is composite, we can use Fermat's Little Theorem for primality testing. The theorem states that if p is a prime number and a is any positive integer less than p, then

\(a^(p-1) ≡ 1 (mod p).\)

Let's take a positive integer a = 2 as our witness. We need to calculate\( 2^(53586077-1) mod 53586077\) and check if it's equal to 1.

\(2^(53586076) mod 53586077 = 3639153\) (using a calculator or software)

Since 3639153 is not equal to 1, this shows that 53586077 is composite, and 2 is a valid witness.

For the Carmichael number 294409, we need to find a nontrivial square root of 1 modulo 294409. A nontrivial square root of 1 is an integer x such that x^2 ≡ 1 (mod 294409) and x ≠ 1 or x ≠ -1 (mod 294409).

Let's take a = 3 as our witness. We need to calculate 3^((294409-1)/2) mod 294409:

\(3^147204 mod 294409 = 1\) (using a calculator or software)

Now, we need to find 3^((294409+1)/2) mod 294409:

\(3^147205 mod 294409 = 294408 \)(using a calculator or software)

Since 1 and 294408 are the trivial square roots of 1 (mod 294409), 3 is not a valid witness for this Carmichael number. However, using trial and error with other witnesses, we can eventually find a nontrivial square root of 1, proving that 294409 is composite.

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There were 29 individuals in the study. The sample size can be calculated by adding 1 to the degrees of freedom (df) represented in the t-statistic.

In this case, df = 28, so 28 + 1 = 29. The report should state that p < .05, which means that the difference between treatments is statistically significant at the 5% level of significance. This indicates that there is less than a 5% chance of observing such a large difference between treatments by chance alone.

However, it is important to note that statistical significance does not necessarily imply practical significance, and the effect size should also be considered when interpreting the results of the study.

Additionally, the report should provide more information about the study design, measures, and variables to give readers a better understanding of the findings and their implications.

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Answer:

Read below

Step-by-step explanation:

For the first row, the inequality is x ≤ -5.

For the second row, the inequality is x < -5.

For the last row, the inequality matching the graph is x ≥ -5.

A trick to remember the sign is if the point on the graph is empty, then the sign would be either < or >, and if it's filled, it would be ≤ or ≥.

Also, x is less is on the left (negative) and x is more is on the right (positive).

Twenty percent of the students in a class of 400 are planning to go to graduate school. The standard deviation of this binomial distribution is 8.

The binomial distribution is a type of probability distribution that computes the probability of a given number of successes in a fixed number of independent tests with two possible results: success and failure. Furthermore, the following are the features of the binomial distribution:

The trial is identical, with two possible outcomes: success and failure.

The probability of success (p) and failure (q = 1 - p) remains constant throughout the trials.

All trials are independent of one another.

The formula for a standard deviation for binomial distribution is given by:

\($\sqrt{npq}$$\)

Where n is the sample size, p is the probability of success, and q is the probability of failure.

Therefore, given that the percentage of students planning to go to graduate school is 20%, the probability of success (p) is 0.2, and the probability of failure (q) is 0.8. The sample size (n) is 400.

Thus, the standard deviation can be calculated as follows:

\($$\sqrt{npq} = \sqrt{400\times 0.2\times 0.8} \approx 8$$\)

Therefore, the standard deviation of this binomial distribution is 8.

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Answer:

Any value of D would make this equation true (-∞,∞)

Answer:

infinitely many solutions

Step-by-step explanation:

i ready

Answer:

10

Step-by-step explanation:

To obtain the length of the segment :

a² + b² = c²

a = 8 ; b = 6

8² + 6² = c²

64 + 36 = c²

100 = c²

Square root of both sides :

Sqrt(100) = sqrt(c²)

10 = c

Mistake in the solution is that 6² = 36 and not 12

Therefore, You can add approximately 0.228 gallons of water to the mix and still remain within the specified W/C ratio of 0.45.

The total weight of the mix is 22 + 41 + 57 + 8 = 128 lbs. To calculate the current W/C ratio, we need to convert the weight of water to gallons. One gallon of water weighs approximately 8.34 lbs. Therefore, the current weight of water is 8/8.34 = 0.96 gallons. The current W/C ratio is 0.96/128 = 0.0075. To remain within spec with a W/C ratio of 0.45, we can use the formula: (water weight + x)/(total weight) = 0.45, where x is the additional weight of water needed. Solving for x, we get x = (0.45 x 128) - 8 = 50.4 lbs. Converting to gallons, this is 50.4/8.34 = 6.05 gallons. Therefore, 6.05 gallons of water can be added to the mix and still remain within spec.
To determine how many gallons of water can be added to the mix and still remain within the specified W/C ratio of 0.45, follow these steps:
1. Calculate the required amount of water for the specified W/C ratio: Cement weight x W/C ratio = 22 lbs. x 0.45 = 9.9 lbs. of water.
2. Subtract the initial water content from the required amount: 9.9 lbs. - 8 lbs. = 1.9 lbs. of additional water needed.
3. Convert the additional water weight to gallons: 1.9 lbs. / 8.34 lbs./gallon (water density) ≈ 0.228 gallons.

Therefore, You can add approximately 0.228 gallons of water to the mix and still remain within the specified W/C ratio of 0.45.

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When dealing with multiplications and divisions only, start calculating from left to right.

Multiply 12 times (0.25):

Multiply 3 times -8:

Notice that in the problem's procedure, the "-" sign was not included in the calculation.

Divide -24 by 1:

Divide -24 by 3:

Multiply -8 by 5:

The final answer is -40.

Answer:

$7

Step-by-step explanation:

We know

SALE 75% OFF!

100% - 75% = 25%

So, the soup pot is now only 25% of its original price.

25% = 0.25

28 times 0.25 = $7

So, Dominic will pay $7 if he buys it during the sale.

The next term of the arithmetic sequence 39, 60, 81, 102, 123, . . . is given by the rule 18 + 21T, where T is any natural number.

An arithmetic sequence is the series where the difference between any two terms is given to be constant.

Here the given arithmetic sequence is,

39, 60, 81, 102, 123, . . .

First term = a = 39

Common Difference = d = 60 - 39 = 21

So, next term,

= 6 th term

= 5 th term + Common Difference

= 123 + 21

= 144

For, any term,

Tth Term = first term + (T-1)Common difference.

Tth Term = 39 + (T-1)21

Tth Term = 39 + 21T - 21

Tth Term = 18 + 21T

So, the rule is 18 + 21T.

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Answer: first answer is C second answer is 144

Step-by-step explanation:

edge 2023

Answer:

A = 35
B = 100
C = 25

Step-by-step explanation:

All interior angles in a triangle add up to 180 degrees.
x + 65 + x + 25 = 180
2x + 110 = 180
2x = 70
x = 35

Answer (1):

A=45 B=110

Step-by-step explanation (1):

So the inner degrees has to equal 180.  So you would do this:

\((x+65)+x+25=180\\2x+90=180\\2x=90\\x=45\)

Now substitute 45 for x and check.

\(45+65=110\\110+45+25= < ABC\\180= < ABC\)

Answer (2):

126 degrees.

Step-by-step (2):

Like I said before, the inner degrees has to equal 180.  We would write another equation.  By the way, the red square is for 90 degrees.

\((5x-6)+3x+90=180\\8x+84=180\\96=8x\\x=12\)

Now substitute 12 for x.

Also to find the anterior angle, we would add the 90 and the 3x\(3(12)=36\\90+36=126\\126+(5x-6)=180\\120+5x=180\\180=180\)

The expected value is the long-term average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and summing them up. In simpler terms, it represents the average value we expect to get over many trials.

The expected value is a concept in probability and statistics that represents the long-term average outcome of a random variable. It is also known as the mean or average. To calculate the expected value, we multiply each possible outcome by its probability and sum them up.

For example, let's say we have a fair six-sided die. The possible outcomes are numbers 1 to 6, each with a probability of 1/6. To find the expected value, we multiply each outcome by its probability:

Summing up these values gives us:

1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5

Therefore, the expected value of rolling a fair six-sided die is 3.5. This means that if we roll the die many times, the average outcome will be close to 3.5.

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