HELP ASAP WORTH MANY A POINTS
the rest of the third question

The amount of space available to tigers in a wildlife refuge changes as the population changes. The graph shows the available territory in a tiger wildlife refuge as a function time since the refuge opened.
Which statements are true about the function?
Select each correct answer.

Given:

The number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation:

\(x=1000-100p\)

To find:

The selling price if the company wants the weekly revenue to be $1,600.

Solution:

We know that the revenue is the product of quantity and price.

\(R=xp\)

\(R=(1000-100p)p\)

\(R=1000p-100p^2\)

We need to find the value of p when the value of R is $1600.

\(1600=1000p-100p^2\)

\(1600-1000p+100p^2=0\)

\(100(16-10p+p^2)=0\)

Divide both sides by 100.

\(p^2-10p+16=0\)

Splitting the middle term, we get

\(p^2-8p-2p+16=0\)

\(p(p-8)-2(p-8)=0\)

\((p-8)(p-2)=0\)

Using zero product property, we get

\(p-8=0\) or \(p-2=0\)

\(p=8\) or \(p=2\)

Therefore, the smaller value of p is $2 and the larger value of p is $8.

Using the slope of the linear function, it is found that Mr. Mole descends 2.3 meters per minute.

A linear function is modeled by:

y = mx + b

In which:

In this problem, Mr. Mole's altitude in meters after t minutes is given by:

A = -2.3t - 7.

The rate of change is the slope of m = -2.3, hence, Mr. Mole descends 2.3 meters per minute.

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Answer:y =-3x/4+2

Step-by-step explanation:

Slope= -3/4

The line is passing through (0,2).

y-2=(x-0)*-3/4

or

y =-3x/4+2

Answer:

\(\Large \boxed{\mathrm{B}}\)

Step-by-step explanation:

\(\sf 5 = -2(x - 1)\)

Applying the distributive property.

We distribute the -2 to the terms in the brackets on the right side of the equation to get Equation B.

\(\sf 5 = -2(x) -2(-1)\)

\(\sf 5 = -2x + 2\)

To get Equation B from Equation A, we rewrite one side or both using the distributive property.

Answer:

C. Adding 18 to both sides isolates the variable term

Step-by-step explanation:

We can get rid of A and C because we can clearly see that we are adding, not subtracting.

The reason why C is correct is because we are isolating 6x, the term, and not x, the variable.

Given, Aika is building a square garden. She places a garden post at (3.5, 3.5)

To find: The location of the corner that reflects (3.5, 3.5) across the y-axis.

We know that the y-axis is the vertical line through the point (0,0) and it divides the plane into two parts: left and right. When we reflect a point across the y-axis, the x-coordinate changes sign. For example, the reflection of (2,3) is (-2,3).Therefore, the reflection of (3.5, 3.5) across the y-axis is (-3.5, 3.5)

Since Aika is building a square garden, the corner opposite to (3.5, 3.5) will have coordinates (-3.5, -3.5).

Hence, the location of the corner that reflects (3.5, 3.5) across the y-axis is (-3.5, -3.5).

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Answer:

for question 2

x^2=102_2

x^2=100

x=10

The amount of the first monthly payment that goes is $845.26.

The monthly payment for a 30-year mortgage of $225,000 at 5.6% interest is $1,126.35. This can be calculated using the following formula:

monthly payment = principal * (interest / 12 / 100) / (1 - (1 + interest / 12 / 100) ** -30)

Plugging in the values for the principal, interest rate, and number of years, we get:

monthly payment = 225,000 * (5.6 / 12 / 100) / (1 - (1 + 5.6 / 12 / 100) ** -30) = 1,126.35

The amount of the first monthly payment that goes towards the principal is 75% of the monthly payment, or $845.26. This can be calculated using the following formula:

principal payment = monthly payment * 0.75

Plugging in the value for the monthly payment, we get:

principal payment = 1,126.35 * 0.75 = 845.26

Therefore, the amount of the first monthly payment that goes towards the principal is $845.26.

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When a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

A double-napped cone is formed by rotating a straight line around another straight line that is parallel to it.

The intersection of a plane with a double-napped cone is referred to as a conic section. A degenerate conic section is formed when a plane intersects a double-napped cone at the vertex.

Thus, when a plane passes through the vertex of a double-napped cone, the intersection is a degenerate conic section.

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Answer:

No

Step-by-step explanation:

Prime numbers have to be only divisible by one and themselves (2 numbers), but one is,\(1*1\) so it is only divisible by one number, thus it is not prime.

Answer:

18 servings

Step-by-step explanation:

If one serving is 1/3 cup, one cup is 3 servings. Therefore, we can multiply 3 x 6 for an answer of 18 servings

First, since the diameter of the pool cover is 18ft, the circumference can be found with the following equation:

then, the circumference is:

next, we can find the area with the following formula:

since the radius of the pool cover is 9 ft, we have:

therefore, the circumference is 56.52ft and the area is 254.34ft^2

Longest object that will fit inside a cylinder will have 12.1 inches.

Lets try to determine the length of the longest object that will fit inside a cylinder with a radius of 21/4 inches and a height of 6 inches,

We will first calculate the diameter and then the diagonal of the cylinder. Afterward, we will calculate the length of the longest object that can be fitted inside the cylinder.

Calculating the diameter

The diameter of a cylinder is double the radius.

Hence, d = 2r, where d is the diameter and r is the radius.

Therefore,

d = 2(21/4)= 42/4= 10.5 inches where r =21/4

The diagonal of a cylinder can be calculated by finding the length of the diagonal of a rectangle with length equal to the height and width equal to the diameter. Since the height of the cylinder is given as 6 inches, and the diameter is 10.5 inches, we can determine the diagonal of the rectangle using the Pythagorean theorem.

Diagonal of rectangle = √(Height² + Width²)

Diagonal of rectangle = √(6² + 10.5²) = √(36 + 110.25)

= √146.25 inches ≈ 12.1 inches

Calculating the length of the longest object that can be fitted inside the cylinder-

The longest object that can be fitted inside the cylinder is the diagonal of the cylinder, which is equal to the diagonal of the rectangle

Diagonal of cylinder = diagonal of rectangle = √146.25 inches ≈ 12.1 inches

Therefore, the length of the longest object that will fit inside a cylinder that has a radius of 21/4 inches and is 6 inches high is approximately 12.1 inches.

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Answer:

Step-by-step explanation:

Part A: Based on the given graph, we can observe that as the temperature of the city increases, the number of people at the swimming pool generally tends to increase as well. This suggests a positive correlation between temperature and the pool's population. In other words, when it gets hotter, more people are likely to visit the swimming pool. The relationship is not strictly linear, but it shows a general trend of increasing pool population with increasing temperature.

Part B: To determine the line of best fit, we can calculate the approximate slope and y-intercept using the given data points. Let's select two points from the data, such as (2.5, 1) and (12, 12):

Slope (m) = (change in y) / (change in x)

= (12 - 1) / (12 - 2.5)

= 11 / 9.5

≈ 1.16

To find the y-intercept (b), we can choose one of the points and substitute the values into the slope-intercept form (y = mx + b). Let's use the point (2.5, 1):

1 = 1.16 * 2.5 + b

1 = 2.9 + b

b ≈ -1.9

Therefore, the approximate slope of the line of best fit is 1.16, and the approximate y-intercept is -1.9.

The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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Therefore, if the students earned $420 for the trip and want to allocate the money equally between the three items, they would be able to spend approximately

How much can student spend admission?

a. Admissions:  If the students plan on visiting a theme park or museum that charges admission, we need to know the cost of each admission ticket. Let's say each admission ticket costs $25. In this case, the students would be able to purchase 16 admission tickets, or spend $26.25 per admission ticket if they plan on purchasing fewer tickets.

How much can student spend food?

b. Food:     Again, we need to know how many meals the students plan on purchasing and the cost of each meal. Let's say the students plan on purchasing 3 meals at an average cost of $15 per meal. In this case, the students would be able to spend $45 on food, or $15 per meal if they plan on purchasing fewer or more expensive meals.

How much can student spend souvenirs?

c. Souvenirs:     Finally, we need to know what kind of souvenirs the students plan on purchasing and how much they cost on average. Let's say the students plan on purchasing 2 souvenirs at an average cost of $20 per souvenir. In this case, the students would be able to spend $40 on souvenirs, or $20 per souvenir if they plan on purchasing fewer or more expensive souvenirs.

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a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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Answer:

x>-6, x<-4

Step-by-step explanation:

|x+5|>-1

x+5>−1 (Possibility 1)

x+5−5>−1−5 (Subtract 5 from both sides)

x>−6

x+5<−(−1)(Possibility 2)

x+5<1(Simplify both sides of the inequality)

x+5−5<1−5(Subtract 5 from both sides)

x<−4

x>-6 or x<-4

We can conclude that the amount of corrosion depends on the coating used, but not on the type of soil. Specifically, coatings 1, 3, and 4 are more effective than coating 2 in reducing corrosion.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To investigate whether the amount of corrosion depends on the coating or on the type of soil, we can perform a two-way ANOVA (analysis of variance) with replication.

The null hypothesis for the ANOVA is that the means of the corrosion depths are equal for all combinations of coating and soil type. The alternative hypothesis is that at least one mean is different from the others.

The ANOVA table shows that there is a significant effect of coating on the corrosion depth since the p-value for coating is less than 0.05. However, there is no significant effect of soil type, since the p-value for soil type is greater than 0.05. The p-value for the interaction term (coating by soil type) is also not significant.

Since there is a significant effect of coating, we can perform posthoc tests to determine which coatings are significantly different from each other. One commonly used posthoc test is the Tukey HSD (honestly significant difference) test. The results of the Tukey test are presented in the table below:

Comparison                     Difference in means Standard error p-value

Coating 1 - Coating 2                   11.0                2.479         0.005

Coating 1 - Coating 3                   14.0                2.479        <0.001

Coating 1 - Coating 4                   13.0                2.479        <0.001

Coating 2 - Coating 3                    3.0                2.479          0.730

Coating 2 - Coating 4                    2.0                2.479          0.947

Coating 3 - Coating 4                   -1.0                 2.479          1.000

The Tukey test shows that coatings 1, 3, and 4 are significantly different from each other, but coating 2 is not significantly different from any of the other coatings.

Therefore, we can conclude that the amount of corrosion depends on the coating used, but not on the type of soil. Specifically, coatings 1, 3, and 4 are more effective than coating 2 in reducing corrosion.

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Answer:

120

Step-by-step explanation:

5!, called 5 factorial is the product of all positive intergers from 5 down though 1. by definition, 0! is 0.

Factorials are basically the number times itself-1 the 2 the 3 until it times it by itself-(itself-1). n!=n*(n-1)*n(n-2).....*n-(n-1).

For example 2!=2*1=2 and 6!=6*5*4*3*2*1=720

keep in mind that I am not an expert so the blanks I filled in might be wrong and the explanation might have errors

5!, called "5 factorial," is the product of all positive integers from 5 down through 1. By definition, 0! is equal to 1.

Factorial is a mathematical operation denoted by an exclamation mark (!). It represents the product of all positive integers from a given number down to 1. In the case of 5!, it is calculated as 5 × 4 × 3 × 2 × 1, resulting in the value of 120.

The exclamation mark notation allows us to represent the factorial of a number concisely. For example, 5! represents the factorial of 5. It is important to note that 0! is defined to be equal to 1. This is a special case in factorial calculations. While it may seem counterintuitive, it is defined this way to maintain consistency and enable certain mathematical calculations and formulas.

Therefore, 5! is the product of all positive integers from 5 down through 1, equaling 120, and 0! is defined to be 1.

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Answer:

Step-by-step explanation:

V =πr²h                              Volume of cylinder

200 = πr²h                         Substitute V = 200

\(\sf \dfrac{200}{\pi r^2} =h\)                               Make the subject as h

\(\sf SA = 2\pi r^2 + 2\pi rh\)               Total Surface area of cylinder

\(\sf SA = 2\pi r^2 + 2\pi r*\left(\dfrac{200}{\pi r^2}\right)\)   Plugin the value of h from step 3

r = 3.169 cm                       Using the graph find the value of r

\(\sf h = \dfrac{200}{\pi *3.169^2} = 6.34 \ cm\)        Substitute the value of 'r' and find the h value          

Answer:

720

Step-by-step explanation:

Given the data:

Minutes ___0___3 ____6____a____12

W/typed__ 0___120 __ ____360 __480

If number of words typed is proportional to number of minutes

Word typed α number of minutes

Word typed = k * number of minutes

k = constant of proportionality

Take

120 = k * 3

k = 120/3 ; k = 40

If test is 18 minutes long ;

Word typed = k * 18

Word typed = 40 * 18

Word typed = 720

The value of x is 6 and the measure of angle LJK is 27°.

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

We have the measure of the following angles,

m∠JKL = ( 3x - 16 )°

m∠LJK = ( 2x + 15 )°

m∠KLM = ( 8x - 19)°

In ΔJKL, JL is extended through point L to point M.

At point L, the measure of angle JLK will be as,

m∠KLM + m∠JLK = 180°

m∠JLK = 180° - m∠KLM

m∠JLK = 180° - ( 8x - 19)°

m∠JLK = ( 199 - 8x )°

Now,

In triangle JKL,

By angle sum property:

m∠JKL + m∠LJK + m∠JLK = 180°

(3x – 16)° + (2x + 15)° + ( 199 - 8x )° = 180°

- 3x + 198 = 180

- 3x = - 18

x = 6°

Therefore,

m∠LJK = ( 2x + 15 )°

m∠LJK = ( 2(6) + 15 )°

m∠LJK = ( 12 + 15 )°

m∠LJK = 27°

The measure of angle LJK is 27°.

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Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

Answer:

True.

Step-by-step explanation:

That is exactly what a perimeter is. Hope this helps

Answer:

∠T

Step-by-step explanation:

∠T is the common angle found in both triangles.

In ΔPTS, ∠PTS represents ∠T.

In ΔQTR, ∠T is represented by ∠QTR.

Answer:

The angle T is common side.

Step-by-step explanation:

Given triangles,

→ ∆PTS & ∆QTR

Now we have to,

→ fInd common angle of both triangles.

The common angle is,

→ <T (angle T)

→ As it is present in both triangles.

Hence, the common part is angle T.