Let x represent the paper 1 score (out of 40) and y
represent the predicted paper 2 score (out of 100).
Which correctly states the equation for the least-
squares regression line and the interpretation of its
slope?

Answer:

x=-3,y =4 z=-1

Step-by-step explanation:

x+2y-5z=10

y+2z=2

z=-1

Since z = -1, substitute into the second equation

y + 2(-1)=2

y -2 =2

y = 2+2

y=4

We can substitute into the first equation

x+2(4) -5(-1) =10

x+8+5=10

x+13 = 10

x = 10-13

x=-3

Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Answer:

12.56m²

Step-by-step explanation:

So the formula for the circumference of a circle is π x diameter, so we just have to plug into our equation (we're using 3.14 as π):

3.14 x 4 = 12.56

So the circumference of your circle is 12.56 meters²

hope this helps:)

Answer:

(x-3) (x-4)/(x-4)

x(x-4)-3 (x-4)/(x-4)

this is the answer!

if you have any problem tell me I will help you

Answer:

the answer is on the picture

Answer:

94%

Step-by-step explanation:

4,700/5,000 x 100%

0.94 x 100% = 94%

Answer:

94%

Step-by-step explanation:

Using the distance formula, the length of segment PQ is:

C. √68 units

The distance formula is given as:

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Segment PQ has the following endpoints:

P(-2, 3)

Q(6, 1)

To find the length of segment PQ using the distance formula, we can apply the formula, where:

\((x_1, y_1)\)are the coordinates of point P

\((x_2, y_2)\) are the coordinates of point Q.

Given:

P(-2, 3) = \((x_1, y_1)\)

Q(6, 1) = \((x_2, y_2)\)

Let's substitute the values into the formula:

PQ = √[(6 - (-2))² + (1 - 3)²]

PQ = √[(8)² + (-2)²)

PQ = √(64 + 4)

length of segment PQ = √68 units

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Answer:

The answer would be 51

Answer:

re send it

Step-by-step explanation:

ty

Complete Question

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 40 girls and 40 boys in a community and gave them the standard memory test. The mean score for girls was 68 and the standard deviation of mean was 5.0. The mean score for boys was 66 and the standard deviation of mean was 5.0. What is the p-value and your conclusion at alpha 0.05

Answer:

The p-value is  \(p-value =0.073614\)

 The conclusion is  

There is sufficient evidence to support the claim  that there was no significant difference between boys and girls on a standard memory test

Step-by-step explanation:

From the question we are told that

      The sample size of boys and girls is  \(n_1= n_2 = n = 40\)

      The standard deviation is  \(s_1= s_2 = s = 5\)

        The level of significance is  \(\alpha = 0.05\)

       The sample mean for boys is  \(\= x_1 =66\)  

The null hypothesis is  \(H_o : \mu_1 = \mu_2\)

The alternative hypothesis is  \(H_a : \mu_1 < \mu_2\)

 Generally the test statistics is mathematically represented as

           \(z = \frac{\= x_1 - \= x_2 }{ \sqrt{\frac{s_1 ^2 }{n_1} + \frac{s_2 ^2 }{n_1} } }\)

=>       \(z = \frac{66 -68 }{ \sqrt{\frac{5^2 }{40} + \frac{5 ^2 }{40} } }\)

=>       \(z = -1.789\)

From the z table  the area under the normal curve to the left corresponding to    -1,789   is

          \(P(Z < -.1789 ) = 0.036807\)

Generally the p-value is mathematically represented as

         \(p-value = 2 P(Z < -.1789 )\)

=>      \(p-value = 2 * 0.036807\)

=>      \(p-value =0.073614\)

From the values obtained we see that  \(p-value < \alpha\) hence

The decision rule is  

Fail to reject the null hypothesis

 The conclusion is  

There is sufficient evidence to support the claim  that there was no significant difference between boys and girls on a standard memory test

Using the probability concept, it is found that there is a \(\frac{7}{20}\) probability that the three segments chosen could form a triangle.

A probability is the number of desired outcomes divided by the number of total outcomes.

Combination formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Total outcomes:

3 segments from a set of 6 lengths, hence:

\(C_{6,3} = \frac{6!}{3!3!} = 20\)

Desired outcomes:

Then:

\(p = \frac{D}{T} = \frac{7}{20}\)

\(\frac{7}{20}\) probability that the three segments chosen could form a triangle.

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Answer:

( 1/x-5)*8x

(1*8x)/(x-5)

8x/x-5

Answer:

Jordan, Its been 5 hours, whats the answer?

Step-by-step explanation:

There can be only 1 triangle formed by the given information.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Given that, ABC can be formed if C=60∘, c=17√3 and a=34

Using the sine law for triangle,

A/sina = B/sinb = C/sinc

34/sina = 17√3/sin60°

⇒ sina = 90°

Since, The triangle ABC is a right triangle,

Hence, There can be only 1 triangle formed by the given information.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Answer:

Step-by-step explanation:

Geometric sequence.

Each term is obtained by multiplying 2. So, it is geometric sequence

2 = 1*2

4 = 2*2

8 = 4 *2

16 = 8 *2

We need to know the relation between height, time to solve this problem. The time taken by the object to be 6 feet above the valley floor is 25 seconds.

The distance an object falls is proportional to the time it took to fall because of gravitational force. Here we have been given an equation that shows us the relation between height of the object and the time taken to reach that height. We know that the initial height of the object is 406 feet, if we substitute the initial height in the equation we get time to be zero which shows us that this is the initial height. We need to find out the time taken by the object to be 6 feet above the valley floor.

h= -16t+406

6=-16t+406

-400=-16t

t=400/16=25 seconds

Therefore the time taken by the object to be at a height 6 feet above the valley floor is 25 seconds.

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The correct option is A, we have a translation of 7 units to the right.-

To find it, we need to analyze two correspondent vertices.

We can see that vertex A is at (1, 5), while the correspondent vertex A' is at (8, 5)

Taking the difference between that, we will get:

A' - A = (8, 5) - (1, 5) = (8 - 1, 5 - 5) = (7, 0)

The first value gives the horizontal translation and the second the vertical one

So,we have a translation of 7 units to the right, the correct option is A.

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The transformations that change the domain of a function are given as follows:

The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.

Hence we must look at transformations that change the values of x of the function, which are given as follows:

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Linear regression will be y = 1.5 + 0.95x.

At first we have to create the following table , to find the values of x , y , x² , xy .

Linear regression is given by y = a + bx  

Then we have to find the value of b using the formula ,

b = n∑xy -( ∑x)(∑y) / n∑x² - (∑x)²

b = 4 X 144 -20 X 25 / 4 X 120 - 400

b = 0.95

Then we have to calculate the value of a using the formula ,

a = ∑y∑x² - ∑x∑xy / n(∑x²) - (∑x)²

a = 25 X 120 - 20 X 144 / 4(120) - 400

a = 1.5

Linear regression is given by y = a + bx  

y = 1.5 + 0.95x.

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Answer:

60+30=90 degrees = complementary angles.

Step-by-step explanation:

Answer:

\(Length = 18m\)

\(Width = 10m\)

Step-by-step explanation:

Given

\(Area = 180m^2\)

\(Width = Length - 8\)

Required

Determine the Length and the Width

Represent Width with W and Length with L;

So, we have:

\(Area = L * W\)

\(Area = L * (L - 8)\)

\(180 = L * (L - 8)\)

\(180 = L^2 - 8L\)

\(L^2 - 8L - 180 = 0\)

Expand

\(L^2 - 18L + 10L- 180 = 0\)

\(L(L - 18) + 10(L- 18) = 0\)

\((L + 10)(L- 18) = 0\)

Split

\(L + 10 =0\) or \(L - 18 = 0\)

\(L = -10\) or \(L = 18\)

But length cant be negative:

So,

\(L = 18\)

Recall that:

\(Width = Length - 8\)

\(W = 18 - 8\)

\(W = 10\)

Hence:

\(Length = 18m\)

\(Width = 10m\)

The dimension of the rectangular garden is 8m by 10m

The formula for calculating the area of the rectangular garden is expressed as;

A = lw

l is the length

w is the width

If the width of the garden must be 8 meters less than the length, then;

w = l - 8

Substitute into the formula;

180 = l(l-8)

180 =l^2 - 8l

l^2-8l - 180 = 0

Factorize the result;

l(l+10)-8(l+10) = 0

(l-8)(l+10)=0

l = 8 and -10

Since A = lw

w = A/l

w = 180/8

w = 10

Hence the dimension of the rectangular garden is 8m by 10m

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Answer:

28

Step-by-step explanation:

C or B's so 30% + 40% = 70% so:

70/100 multiplied by 40 because 40 students

7/10 times 40 = 28

Each person buys a number of cakes

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Andy buys x cakes, Betty buys 4 times as many cakes as andy, and colin buys 3 more cakes than andy

So,

Andy has = x Cakes

Betty have = 4x Cakes

Clin has = x +3 Cakes

Since each cake costs 65p and the total cost of the cakes is £52.65

thus,

0.65( x + 4x + x +3) = 52.62

x + 4x + x +3 = 81

6x = 78

x = 13

Therefore,

Andy has = 13 cakes

Betty has = 4x = 4*13 = 52 cakes

Colin has = x + 3 = 16 cakes

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The writing in red is correct. The inequality sign flips when we divide both sides by a negative value.

To see why the sign flips, think of it like this:

\(-2|x-3| > 0\\\\-2y > 0\\\\-2y+2y > 0+2y\\\\0y > 2y\\\\0 > 2y\\\\2y < 0\\\\2|x-3| < 0\\\\\)

Where \(y = |x-3|\) is used to condense things a bit.

In short, we go from \(-2|x-3| > 0\\\\\) to \(2|x-3| < 0\\\\\) and we have a sign flip.

The '2' is never negative, and same goes for \(|x-3|\). So overall, the entire left hand side is never negative. So there are no solutions to \(2|x-3| < 0\)which further means there are no solutions to \(-2|x-3| > 0\)

Put another way, the original inequality has its left side always as some negative number (assuming x is not equal to 3). There's no way to have a negative number larger than 0. So we have a contradiction leading to no solutions.

Answer:

125

Step-by-step explanation:

5^3 = 5*5*5

5*5*5 = 25*5 = 125

Hope this helps :)

Have a nice day!

Answer:

125

Step-by-step explanation:

5^3 = 5*5*5

5*5*5 = 25*5 = 125

Answer:

The area of the kite is 27.6 cm²

Step-by-step explanation:

Given;

dimension of the equilateral triangle, = 6 cm

dimension of the isosceles triangle = 5 cm

Please check the image uploaded for a detailed solution.

The value of m ∠ABD will be;

⇒ ∠ ABD = 50°

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

In the diagram, the parallel lines are cut by transversal BC.

And,  BD bisects ∠ABC and m∠3 = 80.

Now,

Since, The parallel lines are cut by transversal BC.

Hence, We get;

⇒ ∠ 3 + ∠ 2 = 180°

⇒ 80° + ∠ 2 = 180°

⇒ ∠ 2 = 180 - 80

⇒ ∠ 2 = 100

And, We have;

⇒ ∠ 2 = ∠ ABC

⇒ ∠ ABC = 100°

Since, BD bisects ∠ABC.

Hence, We get;

⇒ ∠ ABD = 100 / 2

⇒ ∠ ABD = 50°

Thus, The value of m ∠ABD = 50°

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The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer:

You Calculate the primiter to 1.5 and solve it

Answer:

1 3/5 boxes

Step-by-step explanation:

There are 5 1/2-3 9/10 boxes left over. We need to simplify this expression.

First, convert both fractions to improper fractions:

11/2-39/10

Now, convert both fractions to have a common denominator of 10:

11/2*5/5 (note we can only do this because any number over itself is equivalent to 1, so technically this is multiplying the number by 1)

55/10-39/10=16/10

Convert it back into a mixed fraction:

1 6/10=1 3/5 boxes

Answer:

1 3/5 boxes

Step-by-step explanation:

5 1/2=5 5/10

leftover=5 5/10-3 9/10=1 6/10=1 3/5

make sure to take 1 from 5

1=10/10

and add it to 5/10 since cant' take away 9/10