Can someone please help

the slope of the line on the graph is 3 .

Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.

to find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .

the points i m choosing is (-2,0) and (-1,3)

now for finding the slope we will use the formula

m = (y2-y1)/(x2-x1)

m = (3 - 0 ) / (-1+2)

m = 3 / 1

m = 3

so the slope of the line on the graph is 3 .

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The Venn Diagram for showing odd numbers and prime numbers would be :

Odd numbers :

Prime number :

Both prime and odd:

4 is not to be included in the Venn Diagram.

Prime numbers are positive integers that have exactly two distinct divisors, which are 1 and the number itself. In other words, a prime number is a number greater than 1 that is divisible only by 1 and itself.

1 is an odd number but not a prime number. 2 is a prime number but not an odd number. 3 and 5 are both odd and prime numbers.

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The volume of the solid defined by the given double integral is 6 cubic units. The double integral ∫∫(12 − 6y) dAᵣ, where r = [0, 1] × [0, 1], represents the volume of a solid, and its value is 6 cubic units.

To evaluate the given double integral, we can identify it as the volume of a solid and then calculate it accordingly. The integral is:

∫∫(12 − 6y) dAᵣ

where r represents the region defined by [0, 1] × [0, 1].

In this case, the integrand (12 - 6y) represents the height or the value of the function at each point (x, y) in the region. By integrating this function over the region r, we can find the volume of the solid that lies above the xy-plane and beneath the surface defined by the function.

The region r = [0, 1] × [0, 1] corresponds to a square in the xy-plane with sides of length 1 unit. This means that the bounds of integration for x and y are both from 0 to 1.

Therefore, we can rewrite the given integral as:

V = ∫[0, 1] ∫[0, 1] (12 - 6y) dx dy

To evaluate this integral, we integrate with respect to x first and then with respect to y.

The inner integral with respect to x gives:

∫(12 - 6y) dx = (12x - 6yx) evaluated from x = 0 to x = 1

= (12 - 6y) - (0 - 0)

= 12 - 6y

Now, we can integrate the resulting expression with respect to y:

∫[0, 1] (12 - 6y) dy = 12y - 3y^2 evaluated from y = 0 to y = 1

= (12 - 6) - (0 - 0)

= 6

Therefore, the volume of the solid defined by the given double integral is 6 cubic units.

In conclusion, the double integral ∫∫(12 − 6y) dAᵣ, where r = [0, 1] × [0, 1], represents the volume of a solid, and its value is 6 cubic units.

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Answer:

The speed of the car engine is 15.4m/s

Step-by-step explanation:

Given

Power = 2100; when Speed = 15

Required

Find Speed when Power = 2200

The question says power is proportional to square of speed;

Mathematically;

\(Power\ \alpha \ Speed^2\)

Represent Power with P and Speed with S

\(P\ \alpha \ S^2\)

Convert proportion to an equation

\(P\ = \ kS^2\)

Where k is proportionality constant

Make k the subject of formula

\(\frac{P}{S^2} = k\)

When P = 2100 and S = 15

\(\frac{2100}{15^2} = k\)

When P = 2200 and S is unknown

\(\frac{2200}{S^2} = k\)

Recall that \(\frac{2100}{15^2} = k\)

So;

\(\frac{2200}{S^2} = k\) becomes

\(\frac{2200}{S^2} = \frac{2100}{15^2}\)

Cross Multiply

\(S^2 * 2100 = 2200 * 15^2\)

\(S^2 * 2100 = 2200 * 225\)

\(S^2 * 2100 = 495000\)

Divide both sides by 2100

\(S^2 = \frac{495000}{2100}\)

\(S^2 =235.714285714\)

Take Square Roots of both sides

\(S = \sqrt{235.714285714}\)

\(S =15.3529894716\)

\(S = 15.4\) (Approximated)

Answer:

No

Step-by-step explanation:

A function means direct adding patterns on both sides. If you notice, the first one, it goes +1+1+1+1 +3???? which is not correct. It should be +1.

Hope this helps :D  

Answer:

Yes, this is a function, because for every output there is one input!

Step-by-step explanation:

Answer:

155,588

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = growth rate

N = number of years 2021 - 2014 = 7

130,000(1.026)^7 = 155,587.6

rounding off to the nearest whole  number is 155,588

To round off to the nearest whole number, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

a) The sample proportion of U.S. residents over 25 who had a bachelor’s degree or higher is 0.5065

b) Independence: The sample of 77 U.S. residents over 25 must be randomly and independently selected.

c) The 90% confidence interval is: between 39.2% and 62.1%.

a) The sample proportion of U.S. residents over 25 who had a bachelor's degree or higher is calculated by dividing the number of sampled residents with a bachelor's degree or higher by the total number of residents sampled.

Sample proportion = 39/77 = 0.5065 (rounded to four decimal places)

b) The three conditions of the Central Limit Theorem are:

1. Independence: The sample of 77 U.S. residents over 25 must be randomly and independently selected.

2. Sample Size: The sample size must be large enough (n >= 30).

3. Sample Proportion: The sample proportion should not be too close to 0 or 1, which is satisfied as 0.5065 is not too close to either 0 or 1.

c) To construct a 90% confidence interval, we can use the formula:

CI = sample proportion +/- margin of error where the margin of error can be calculated as:

margin of error = critical value ×standard error

The critical value can be obtained from the z-table for a 90% confidence level, which is 1.645.

The standard error can be calculated as: standard error = √(sample proportion × (1 - sample proportion)) / sample size)

Plugging in the values, we get:

standard error = √0.5065 × (1 - 0.5065)) / 77) = 0.0693

Now, we can calculate the margin of error:

margin of error = 1.645 × 0.0693 = 0.114

Therefore, the 90% confidence interval is:

CI = 0.5065 +/- 0.114 = (0.392, 0.621)

So, we can be 90% confident that the true proportion of U.S. residents over 25 who have a bachelor's degree or higher falls between 39.2% and 62.1%.

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In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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"Segment GT is congruent to segment PD on the number line." this statement is True.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

The number line is used to represent the coordinates G, T, Y, B, M, P, D, W.

The point of G is -10 and the point of T is -9.

To get the measurement subtract G from T -

= -9 - (-10)

= -9 + 10

= 1

The point of P is 5 and the point of D is 6.

To get the measurement subtract P from D -

= 6 - 5

= 1

The measurement of GT and PD both is 1.

Therefore, segment GD is congruent to segment PD on the number line.

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Answer:

-15

Step-by-step explanation:

-20 + x = ?

If x = 5, then:

-20 + 5 = -15

Answer:

Coefficient

Step-by-step explanation:

The area of the triangle in front of the triangular prism is xy/2.

The triangular prism is a three-dimensional shape with three rectangular and two triangular faces. The triangular faces are parallel to one another and the rectangular faces are perpendicular to the triangular edges.

The area of a shape is determined by the measurement of the surface of the shape.

The area of a triangle is base multiplied by the height of a triangle divided by 2.

We have to find the area of the front triangle which means the area of the one triangle.

Assume that the base of the triangle is x and the height of the triangle is y

So,

Area of triangle= ½ base×height

                          =  ½ x × y

                          = xy/2

Therefore the area of a triangle  is xy/2

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Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.

To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.

First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:

Principal = $1,000

Rate of interest per period = 8% / 4 = 2% per quarter

Number of periods = 12 quarters

Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)

                           = $1,000 * (1 + 0.02)^12

                           ≈ $1,166.41

Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):

Principal = $1,000

Rate of interest per period = 2% per quarter

Number of periods = 8 quarters

Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)

                         = $1,000 * (1 + 0.02)^8

                         ≈ $1,165.16

Finally, we add the two values to find the total value of the account on January 1, 2021:

Total value = Value after three years + Value after two years

                ≈ $1,166.41 + $1,165.16

                ≈ $2,331.57

Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.

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Answer:

yes

Step-by-step explanation:

15.3-7.9=7.4

Answer: the unit rate is 2.5

Step-by-step explanation:

Answer:

Yes, it is linear. y=-1/2x+3/4

Step-by-step explanation:

To put it in standard form, you need to get the y by itself.

4y=-2x+3

Divide by 4.

y=-1/2x+3/4

Answer:

Yes

Step-by-step explanation:

(X,Y) = (-98,332)

This means that X is -98 and Y is 332

If you substitute the value of y into y = 332, you get 332 = 332 which is true.

Therefore (-98,332) makes the equation y = 332 true.

Megan should put 7 books on each shelf since 42 divided by 6 equals 7. This way, each shelf will have the same number of books and the library will look balanced.

To find out how many books Megan should put on each shelf, the total number of books must be divided by the number of shelves. In this case, 42 books needs to be divided by 6 shelves. To do this, we simply divide 42 by 6. 42 divided by 6 is 7, so Megan should put 7 books on each shelf. This way, each shelf will have the same number of books and the library will look balanced. To check if the calculation is correct, we can multiply 7 by 6 to make sure it equals 42. 7 multiplied by 6 is 42, so we know that the calculation is correct. Therefore, Megan should put 7 books on each shelf to evenly distribute the books in the library.

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Answer:

2 rocks

Step-by-step explanation:

2 crates + 2 rocks = 1 crate + 4 rocks

2 crates + 2 rocks = 2 crates + 8 rocks

Hence, 1 crate = (8-4)÷2

= 2 rocks

Based on the given information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own graphing TI calculators so it can be estimated that the proportion of students who do not own a TI graphing calculator is 50%.

To estimate the proportion of students who do not own a TI graphing calculator, we can use the information provided that out of the 4 students who owned a TI calculator, 2 had graphing calculators. Since we know that all graphing calculators are TI calculators, we can assume that the 2 students with graphing calculators are included in the total count of students who own TI calculators. Therefore, the remaining 2 students who own TI calculators must have non-graphing calculators.

Based on this information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own non-graphing TI calculators. Therefore, we can estimate that the proportion of students who do not own a TI graphing calculator is 50%.

It's important to note that this is an estimation based on the limited information provided. To obtain a more accurate estimate, a larger sample size or more comprehensive data would be needed. Additionally, this estimation assumes that the sample of 4 students is representative of the entire student population in terms of calculator ownership. If there are any biases or limitations in the sampling method or if the sample is not representative, the estimate may not accurately reflect the true proportion of students who do not own a TI graphing calculator.

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Answer:

8.4 is the answer and the circumference is 26.4

Answer: 5 or 9

Find the factors of the number 45.

1, 5, 9, 15

The numbers must be greater than 1 and less than 10.

Now, we must take 5 and 9.

5 x 9 = 45

9 x 5 = 45

The answers are 5 & 9.

Answer: 5, 9

Factors of 45:

5 and 9 are between 1 and 10.

They are the answers.

5 x 9 = 45

9 x 5 = 45

now, we know the angle is in the I Quadrant, where sine and cosine or opposite and adjacent sides are both positive, so

\(\sin(\theta )=\cfrac{\stackrel{opposite}{2}}{\underset{hypotenuse}{\sqrt{7}}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{7}}\\ a=adjacent\\ o=\stackrel{opposite}{2} \end{cases}\)

\(a=\pm\sqrt{ \sqrt{7^2} - 2^2}\implies a=\pm\sqrt{ 7 - 4 } \implies a=\pm\sqrt{ 3 }\implies \stackrel{ I~Quadrant }{a=+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\theta )=\cfrac{\stackrel{opposite}{2}}{\underset{adjacent}{\sqrt{3}}}\hspace{9em} \stackrel{\textit{Double Angle Identities}}{\tan(2\theta)=\cfrac{2\tan(\theta)}{1-\tan^2(\theta)}}\)

\(\tan(2\theta)\implies \cfrac{2\cdot \frac{2}{\sqrt{3}}}{1-\left( \frac{2}{\sqrt{3}} \right)^2}\implies \cfrac{~~ \frac{4 }{\sqrt{3} } ~~}{1-\frac{4}{3}}\implies \cfrac{~~ \frac{4 }{\sqrt{3} } ~~}{\frac{3-4}{3}}\implies \cfrac{~~ \frac{4 }{\sqrt{3} } ~~}{\frac{-1}{3}} \\\\\\ \cfrac{4 }{\sqrt{3} }\cdot \cfrac{3}{-1}\implies -\cfrac{4\cdot 3}{\sqrt{3}}\implies \boxed{-4\sqrt{3}}\)

Answer:

The highest score is 94.

Step-by-step explanation:

Let the highest score be denoted by, A, the lowest score be, B and the middle score be X.

Then,

A + X + B = 87 × 3 = 261 ...(i)

X + B = 83.5 × 2 = 167 ...(ii)

⇒ B = 167 - X ...(iii)

A + X = 89 × 2 = 178 ...(iv)

⇒ A = 178 - X ...(v)

Substitute (iii) and (v) in (i) and solve for X as follows:

A + X + B = 261

178 - X + X + 167 - X = 261

345 - X = 261

X = 84

Substitute the value of X in (iii) and solve for B as follows:

B = 167 - X

   = 167 - 84

   = 83

Substitute the value of X in (v) and solve for A as follows:

A = 178 - X

   = 178 - 84

   = 94

Thus, the highest score is 94.

Micah's boxplot is incorrect because the statistical summary given by his boxplot is inaccurate.

The boxplot is a better at analysing the data as it gives more statistical output of the data than the histogram.

We need to write out the number of times taken by each student,

From the histogram; the data values are :

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 7, 7, 8, 8, 9, 9, 10, 10, 10

Using a boxplot maker or excel, we could create a boxplot of the data and compare with that given in the question.

5 number summary of Micah's boxplot :

Minimum = 1 (position of lower whisker)

Maximum = 9 (Position of upper whisker)

Lower quartile = 3(starting point of box)

Upper quartile = 8 (endpoint of box)

Median = 5 (vertical line in between box)

Outlier = 10

5 number summary of correct or accurate boxplot :

Minimum = 1 (position of lower whisker)

Maximum = 10 (Position of upper whisker)

Lower quartile = 2 (starting point of box)

Upper quartile = 8.2 (endpoint of box)

Median = 4.5 (vertical line in between box)

Outlier = None

Comparing the box plots, it can be concluded that Micah did not create the boxplot correctly.

Answer:

2<x<3

The chords in the circle L are illustrations of intersecting chords

The lengths that are even numbers are FJ and GJ

The length AD is given as:

AD = 10

From the circle, we have:

AD = AH + HK + KD

Where:

AH = 3 and KD = 2

So, we have:

10 = 3 + HK + 2

Solve for HK

HK = 5 ---- odd length

Next, we calculate length FH using the following intersecting chord theorem

FH * HB = AH * HD

This gives

(FJ + 3) * 3 = 3 * (2 + 5)

Divide by 3

FJ + 3 = 7

Subtract both sides by 3

FJ = 4 --- even length

Next, we calculate length KE using the following intersecting chord theorem

KE * KC = KD * KA

This gives

KE * 3.2 = 2 * (5 + 3)

Evaluate the product

KE * 3.2 = 16

Divide by 3.2

KE = 5 --- odd length

Next, we calculate length GJ using the following intersecting chord theorem

GJ * JE = FJ * JB

This gives

GJ * 4.5 = 4 * (6 + 3)

Evaluate the product

GJ * 4.5 = 36

Divide by 4.5

GJ = 8 --- even length

Hence, the lengths that are even numbers are FJ and GJ

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The experimental and theoretical probabilities for the given experiment are:

i) The experimental probability of rolling a 2 is equal to the quotient between the number of times that the outcome was a 2 and the total number of times that the number cube was rolled, so the probability is:

P = 8/50 = 0.16

ii) The theoretical probability assumes that all the numbers (6) have the same probability of rolling up.

Then all the numbers have a probability of 1/6.

This means that the theoretical probability of rolling a 2 is:

P(2) = 1/6 = 0.167

iii) The experimental probability of NOT rolling a 2 is computed in a similar way than the first one, if out of 50 rolls, in 8 we rolled a 2, then in 42 we did not rolled a 2.

So the probability is:

P = 42/50 = 0.84

iv) The theoretical probability of not rolling a 2 is equal to 1 minus the theoretical probability of rolling a 2.

P = 1 - 1/6 = 5/6 = 0.833...

v) For the experimental probability of getting a 1, we see that out of 50 rolls, in 10 we rolled a 1, so the probability is:

P = 10/50 = 1/5 = 0.2

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Answer:

 \(\frac{x-7}{4} =f^{-1}( x)\)

Step-by-step explanation:

→ Replace f(x) with y

y = 4x + 7

→ Minus 7 from both sides

y - 7 = 4x

→ Divide both sides by 4

\(\frac{y-7}{4} =x\)

→ Replace y's with f⁻¹(x)

\(\frac{x-7}{4} =f^{-1}( x)\)