Define overlapping. ​

There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Null hypothesis (H₀): There is no significant difference between the mean scores of Education and Nursing students in mathematics.

Alternative hypothesis (H₁): There is a significant difference between the mean scores of Education and Nursing students in mathematics.

We will use significance level (α) of 0.01.

Given:

Sample mean for Education students (x₁) = 88.50

Sample mean for Nursing students (x₂) = 90.25

Standard deviation for the Education student sample (s₁) = 7.5

Standard deviation for the Nursing student sample (s₂) = 8.2

Sample size for Education students (n₁) = 25

Sample size for Nursing students (n₂) = 29

The t-test statistic for two independent samples is:

t = (x1₁ - x2) / sqrt((s₁² / n₁) + (s₂² / n₂))

t = (88.50 - 90.25) / sqrt((7.5² / 25) + (8.2² / 29))

t ≈ -0.8187

In this case, df = 24.

The critical value for α = 0.01 and df = 24 is approximately ±2.797.

Since |-0.8187| < 2.797, the absolute value of the t-test statistic is smaller than the critical value.

Therefore, we fail to reject the null hypothesis.

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Answer:

24

Step-by-step explanation:

3+2=5

5u-> 60

1u->12

2u-> 24

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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We can represent a function in four ways: Algebraically, Numerically, Graphically, Visually.

In the given question we have to explain how we represent a function.

A function is a relationship between two sets of variables in which one variable depends on another. Different techniques can be used to portray various sorts of functions. Typically, functions are represented by diagrams or formulas. The four approaches for representing a function are as follows:

Algebraically

Numerically

Graphically

Visually

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Step-by-step explanation:

a) Tangent equals sine divided by cosine.  Therefore:

tan(-t) = sin(-t) / cos(-t)

b) Using the fact that sin(-t) = -sin(t) and cos(-t) = cos(t):

tan(-t) = -sin(t) / cos(t)

tan(-t) = -tan(t)

c) A function is symmetric about the origin if f(-x) = -f(x) (in other words, if it's an odd function).  Therefore, y = tan(t) is symmetric about the origin.

Answer:

The option is  A

Step-by-step explanation:

From the question we are told that

    The population proportion is  \(p =  0.29\)

    The sample size is  n  = 451

    The number that was having difficulty is  k  =  183

Generally the sample proportion is mathematically represented as

     \(\^ {p}  =  \frac{k}{n}\)

=>  \(\^ {p}  =  \frac{183}{451}\)

=>   \(\^ {p}  =   0.4058\)

Generally the test statistics is mathematically represented as

    \(t = \frac{ \^ {p} -  p }{ \sqrt{\frac{p (1-p)}{n} } }\)

=>  \(t = \frac{0.4058 -  0.29 }{ \sqrt{\frac{0.29 (1-0.29)}{451} } }\)

=>  \(t =  5.42 \)

Answer:

x = 13

Step-by-step explanation:

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

Answer:

a

Step-by-step explanation:

4 up 3 across

Answer:

x=2

Step-by-step explanation:

16+4=3x+7x

20=10x

20/10=10x/10

2=x

Answer:

a solid material that is typically hard, shiny, malleable, fusible, and ductile, with good electrical and thermal conductivity ( iron, gold, silver, copper, and aluminum, and alloys such as brass and steel)

Step-by-step explanation:

Answer:

52500

Step-by-step explanation:

first do 5*105 to get 525 then mutiply by 100 to get 52500

Answer:

Step-by-step explanation:

X: -2, -1, 0, 1, 2,...

Y: -2, -1, 0, 1, 2,...

(y=x)

The two equations which can be used to represent the situation are;

r + s = 1787

4r + 3s = 5,792

The correct answer choice is option B and E

Reserved seat for basketball game = r

Students seat for basketball game = s

Cost of reserved seat tickets = $4

Cost of students tickets = $3

Total number of people who attended the basketball game= 1,787 people

Total amount earned for tickets sales= $5,792

r + s = 1787

4r + 3s = 5,792

Therefore, the basketball game situation can be represented by the equation r + s = 1787; 4r + 3s = 5,792

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Answer:

-------------------------------------------

Let's simplify left sides of each statement and compare with right sides:

Answer:

36

Step-by-step explanation:

5 x 4 = 20

20 x 2 = 40

40 x 2 = 80

80 ÷ 2 = 40

40 - 4 = 36

The number of suspects had less than two prior arrests are 3.

Given that, While reviewing the previous day’s arrest report.

Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.

Here, x+y=5 -----(i)

2x+3y=12 -----(ii)

From equation (i), x=5-y in equation (ii), we get

2(5-y)+3y=12

10-2y+3y=12

10+y=12

y=2

Substitute y=2 in equation (i), we get

x+2=5

x=3

Therefore, the number of suspects had less than two prior arrests are 3.

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The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

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Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

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Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.

A function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The independent variable = domain

The dependent variable = Range

We are given a graph where the x-axis contains the radius value and the y-axis contains the circumference value.

We can write the function as:

f(x) where x can be 4, 8, 12, 16, 20, 24, 28, 32, 36

f(0) = 0

f(4) = 22.5

f(8) = 52.5

f(12) = 75

f(16) = 105

f(20) = 127.5

f(24) = 150

The domain is between 0 to 150 and the range is between 0 and 28.

Thus the domain is 0 ≤ Domain ≤ 28 and the range is 0 ≤ range ≤ 150.

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Answer:

3. y=6x/5+7/5

4.y=2x+2

5.

Step-by-step explanation:

Answer:

3) m = 6/5

4) m = 2

5) y = 3x + 2

6) y = -2x - 3

Step-by-step explanation:

To find slope for questions 3 and 4, use formula below⤵⤵⤵

\( \frac{y _{2} - y _{1} }{x _{2} - x _{1}} \)

3) 5-(-1) ➡ 5+1 ➡ 6

3-(-2) ➡ 3+2 ➡ 5

4) -8-4 ➡ -12 ➡ 12 12÷6 = 2

-5-1 ➡ -6 ➡ 6

For questions 5 and 6, find the y-intercept first, which is the point in which the line crosses the y-axis. From then you can use rise/run to find the slope.

Hope this helps :)

By def. of the derivative, we have for y = ln(x),

\(\displaystyle \frac{dy}{dx} = \lim_{h\to0} \frac{\ln(x+h)-\ln(x)}{h}\)

\(\displaystyle \frac{dy}{dx} = \lim_{h\to0} \frac1h \ln\left(\frac{x+h}{x}\right)\)

\(\displaystyle \frac{dy}{dx} = \lim_{h\to0} \ln\left(1+\frac hx\right)^{\frac1h}\)

Substitute y = h/x, so that as h approaches 0, so does y. We then rewrite the limit as

\(\displaystyle \frac{dy}{dx} = \lim_{y\to0} \ln\left(1+y\right)^{\frac1{xy}}\)

\(\displaystyle \frac{dy}{dx} = \frac1x \lim_{y\to0} \ln\left(1+y\right)^{\frac1y}\)

Recall that the constant e is defined by the limit,

\(\displaystyle e = \lim_{y\to0} \left(1+y\right)^{\frac1y}\)

Then in our limit, we end up with

\(\displaystyle \frac{dy}{dx} = \frac1x \ln(e) = \boxed{\frac1x}\)

In Mathematica, use

D[Log[x], x]

Answer:

Rate of travel = 83 miles per day

Step-by-step explanation:

Given:

Total distance = 2,739

Number of days = 33 days

Find:

Rate of travel

Computation:

Rate of travel = Total distance / Number of days

Rate of travel = 2,739 / 33

Rate of travel = 83 miles per day

Elena can make 20/3 cups of purple paint

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.

Since Elena has 2/3 cup of white paint. then;

1 1/2 cups of red paint (1 1/2=1.5)

1/2 cup of white paint (1/2=0.5)

Then the ratio is 3:1.5:0.5

Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)

Let x the number of cups of purple paint

5/ 0.5 = x / (2/5)

x = 20/3 cups of purple paint

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Answer:

1. a 3d rectangle

2. 40 in cubed

3. repeat

4. another repeat

Step-by-step explanation:

Answer:

\(\displaystyle y=\frac{1}{1-4e^{-x}}\)

Step-by-step explanation:

\(\displaystyle y=\frac{1}{1+C_1e^{-x}}\\\\-\frac{1}{3}=\frac{1}{1+C_1e^{-0}}\\\\-\frac{1}{3}=\frac{1}{1+C_1}\\ \\ 3=-1-C_1\\\\4=-C_1\\\\-4=C_1\)

Thus, the specific solution to the IVP given the initial condition is \(\displaystyle y=\frac{1}{1-4e^{-x}}\)