There are 1,523 students at Eden Elementary School, 1,471 students at Logan Elementary School, and 2,697
students at Thomas Elementary School. About how many students are there at the schools altogether?
3,000 students
4,000 students
5,000 students
6,000 students

Answer:

Step-by-step explanation:

The standard form of writing a scientific notation is expressed as \(a.b*10^n\) where a, b and n are integers. Note that a, b and n cannot be a fraction. When writing in scientific notation, the value of 'a' must not be equal to zero and it must not be a 'two digits values' but just 'a digit value'.

Based on the above conclusion, the following numbers are correctly written in scientific notation.

1×10⁻⁴ and 9.8×10⁵

- The expression 10.8×10 −3 is not correctly written because the value of a on comparison is a two digits number i.e 10.

- Also, 0.54×10^6 is not correctly written because a is zero on comparison

- 7.6×10 2.5 is not correctly written because the power is a decimal number i.e 2.5. We must only have an integer as the degree.

Answer:

h(3) = -7

Step-by-step explanation:

h(3) = - 3 - 4 = -7

Answer:

Step-by-step explanation:

The complete solution in radians of the given equation is: θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is an integer.

To find the complete solution in radians of the equation 4 sin²θ + 1 = 4 sinθ, we can first rewrite the equation as a quadratic equation.

Let's substitute sinθ with x for simplicity: 4x² + 1 = 4x

Rearranging the equation: 4x² - 4x + 1 = 0

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, factoring or completing the square won't yield nice solutions, so we'll use the quadratic formula.

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

For our equation: a = 4, b = -4, and c = 1

Plugging these values into the quadratic formula, we get: x = (-(-4) ± √((-4)² - 4(4)(1))) / (2(4))

Simplifying: x = (4 ± √(16 - 16)) / 8

Further simplifying: x = (4 ± √0) / 8

Since the discriminant (√0) is zero, we have only one solution: x = 4/8 = 1/2

Now, we need to find the values of θ that correspond to sinθ = 1/2.

In the unit circle, sinθ = 1/2 occurs at two angles: π/6 and 5π/6 (in the first and second quadrants).

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Answer:

m = 5

Step-by-step explanation:

Since the triangles are similar in the way shown, then

6/10 = 3/m

6m = 10 × 3

m = 5

Answer:

23

Step-by-step explanation:

y=f(n)=( -4× -7)-5

f(n)=28-5 =23

Answer:

The answer is below

Step-by-step explanation:

Since 1000ml Of Dextrose 25% is needed to be produced from Dextrose 70%. Let us assume that x ml of Dextrose 70% is mixed with a Dextrose 5% to get 1000 ml of Dextrose 25%. Hence:

The amount of Dextrose 5% = 1000 ml - x ml = 1000 - x

25% of 1000 ml = 70% of x + 5% of (1000 - x)

25000 = 70x + 5000 - 5x

Simplifying gives:

65x = 25000 - 5000

65x = 20000

x = 308 ml

Therefore 308 ml of Dextrose 70% was mixed with 692 ml of Dextrose 5% to produce 1000 ml of Dextrose 25%.

Answer:

6.1 square units

Step-by-step explanation:

Since the triangle was translated from one position to another position, the dimensions of the triangle have not changed. The pre-image and image are congruent.

area = base * height/2

The two sides forming a right angle can be used as the base and the height in the area formula.

BC = base = 2

AB = A'B' = height = 6.1

area = 2 * 6.1/2

area = 6.1 square units

The solutions are given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Part A

the dotted line formes the thrid side of the triangle.

part B

The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.

part c

If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.

part D

You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.

part e

The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.

part f

Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters

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Answer:

You can buy 8 pizzas

Step-by-step explanation:

$58 - $10 = $48

$48/$6 = 8

The particular solution to the differential equation with the initial condition y(7) = 0 is:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:

Step 1: Write the given differential equation in the form dy/dx = f(x, y).

  In this case, dy/dx = y² - 4.

Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:

  dy / (y² - 4) = dx.

Step 3: Integrate both sides of the equation:

  ∫ dy / (y² - 4) = ∫ dx.

Let's solve each integral separately:

For the left-hand side integral:

Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).

Using partial fractions, we can decompose the left-hand side integral:

1 / (y² - 4) = A / (y - 2) + B / (y + 2).

Multiply both sides by (y - 2)(y + 2):

1 = A(y + 2) + B(y - 2).

Expanding the equation:

1 = (A + B)y + 2A - 2B.

By equating the coefficients of the like terms on both sides:

A + B = 0, and

2A - 2B = 1.

Solving these equations simultaneously:

From the first equation, A = -B.

Substituting A = -B in the second equation:

2(-B) - 2B = 1,

-4B = 1,

B = -1/4.

Substituting the value of B in the first equation:

A + (-1/4) = 0,

A = 1/4.

Therefore, the decomposition of the left-hand side integral becomes:

1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).

Integrating both sides:

∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.

Integrating the right-hand side:

∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy

= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,

where C₁ is the constant of integration.

For the right-hand side integral:

∫ dx = x + C₂,

where C₂ is the constant of integration.

Combining the results:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.

Simplifying the equation:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).

Combining the constants of integration:

C = C₂ - C₁, where C is a new constant.

Finally, we have the solution to the differential equation that satisfies the initial condition:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.

To find the value of the constant C, we use the initial condition y(7) = 0:

(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.

Simplifying the equation:

(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,

(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,

0 = 7 + C,

C = -7.

Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

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Answer:

It will take Janice 48 minutes to run 4 miles.

Step-by-step explanation:

She is running 1 mile every twelve minutes, so 4*12 will give you the answer, which is 48 minutes.

Answer:

\(\frac{12a^7b^5}{16a^2b^2}=\frac{3}{4} a^5b^3\)

The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answer:

Equals

Step-by-step explanation:

Answer:

x²-9x+14

Step-by-step explanation:

So the roots are 2,7

So the equation is

(x-2)(x-7)

=x²-2x-7x+14

=x²-9x+14

Answer:

88 hrs

Step-by-step explanation:

1/3/4 = 7/4hr ; 7/4 = 1.75hr (the number of hours used to travel for 154km)

154/1.75 = 88 (the number of km van travels per hour)

a.she must deposit $219,974.28 today.

b. the balance in the account immediately after the fourth withdrawal will be $215,449.44

c. there will be no balance in the account after all the withdrawals have been made including the last one in six years.

d.if you drop out today, you would have $284,431.85 at the end of six years.

a) The present value formula can be used to calculate the initial deposit. PV = FV / (1 + r) n

Where,PV is present value, FV is future value, r is the interest rate and n is the number of years.Since the future value is known ($45,000 each year for six years) and the interest rate is known (4%), we can calculate the present value as follows.

PV = $45,000 x [1 - 1/(1 + 0.04)^6] / 0.04PV = $219,974.28

Therefore, she must deposit $219,974.28 today.

b) To calculate the balance after four years, we need to calculate the future value of the initial deposit using the following formula:FV = PV x (1 + r) n + PMT x [(1 + r) n - 1] / r

Where,PV is present value, FV is future value, r is the interest rate, n is the number of years and PMT is the payment made each year.

FV = $219,974.28 x (1 + 0.04) ^ 6 + $45,000 x [(1 + 0.04) ^ 6 - (1 + 0.04) ^ 2] / 0.04FV = $215,449.44

Therefore, the balance in the account immediately after the fourth withdrawal will be $215,449.44

.c) After six years, all six withdrawals will be made, so the account balance will be zero. Therefore, there will be no balance in the account after all the withdrawals have been made including the last one in six years.

d) If you decide to drop out today and not make any withdrawals, you will have $219,974.28 in the account after six years.

Therefore, the future value of the initial deposit will be:

FV = PV x (1 + r) n

FV = $219,974.28 x (1 + 0.04) ^ 6

FV = $284,431.85

Thus, if you drop out today, you would have $284,431.85 at the end of six years.

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Using the law of sins:

B =sin^−1((sin(A)⋅a)/b) = sin^−1((sin(65)⋅110)/155)=40.03 degrees

B= 40.03 degrees (round as needed)

Answer:

b) Quad ABCD must be a rectangle and could be a rhombus

Step-by-step explanation:

:)

Answer:

2^-3

Step-by-step explanation:

Answer:

The answer is the second one: \((-1/2)^{-3}\)

Step-by-step explanation:

1) When an exponent is negative, we must 'flip' the term before applying the exponent.

\((-1/2)^{-3}\) = \((-2/1)^3\)= \(-2^3\)

2) Next, we need to cube two. Remember, the negative number does not apply yet!

\(-2^3\) = -8

3) Thus, we get our answer. -8.

I hope this help, firend!!

Another advantage of using Anova is that it arranges the means so the significant differences can be located and interpreted easily.

The ANOVA test is a type of statistical test used to determine whether there is a statistically significant difference between two or more categorical groups by testing mean differences using variance.

Another important part of the ANOVA is the splitting of the independent variables into two or more groups.

The assumptions for the ANOVA test are the same as those for general parametric tests.

Advantages of ANOVA:

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The correct statement is c. The Adjusted R-squared is a measure used in multiple regression analysis that is between 0 and 1. It is different from the R-squared value in simple linear regression.

The Adjusted R-squared can decrease if the addition of another X regressor does not sufficiently lower the sum of squared residuals (SSR) relative to the impact of increasing the number of predictors (k). It measures the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size, rather than the ratio of the sum of squared residuals to the total sum of squares. It provides a measure of how well the regression model fits the data, and it ranges between 0 and 1. A value closer to 1 indicates that a higher proportion of the variance in the dependent variable is explained by the predictors.

Adding another X regressor to the multiple regression model can impact the Adjusted R-squared. If the additional regressor does not significantly contribute to reducing the sum of squared residuals (SSR) relative to the increase in the number of predictors (k), the Adjusted R-squared can decrease. This means that the added regressor does not improve the model's ability to explain the variance in the dependent variable adequately.

However, the Adjusted R-squared does not directly measure the ratio of the sum of squared residuals to the total sum of squares. Instead, it represents the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size. It penalizes models with a large number of predictors that may overfit the data, thereby providing a more reliable measure of the model's goodness of fit.

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The integral of the function can be expressed as (1/5) (sin⁻¹(cos(x)))⁵ - (1/5) (cos⁴(x)/4 + (2/3) cos⁶(x) - (1/9) cos⁸(x)) + C, where C is the constant of integration.

The integral should be evaluated as shown below.∫tan⁴(x) cos⁵(x) dx the substitution be made,u = cos(x), then we obtain/dx = - sin(x) du = - sin(x) dx.Solving for dx, dx = - du/sin(x)Now we substitute the values in the equation as shown below.∫tan⁴(x) cos⁵(x) dx= - ∫(tan⁴(x) / sin(x)) (-sin(x) cos⁵(x))dx= ∫(tan⁴(x) cos⁵(x)) (1/sin(x))dx= ∫((sin⁻¹(u))⁴ u⁵) this integral can be solved by means of parts. To do so, let V = (sin⁻¹(u))⁴ du = 5u⁴/((1 - u²)²)Now we can evaluate the integral as shown below.∫((sin⁻¹(u))⁴ u⁵) du= (1/5) ((sin⁻¹(u))⁵) - (1/5) ∫u⁴ (1 - u²)² duThe definite integral will have the form below after expanding the right-hand side.∫((sin⁻¹(u))⁴ u⁵) du= (1/5) ((sin⁻¹(u))⁵) - (1/5) (∫u⁴ du - 2∫u⁶ du + ∫u⁸ du) + CFinally, let us substitute back u = cos(x).∫tan⁴(x) cos⁵(x) dx= (1/5) (sin⁻¹(cos(x)))⁵ - (1/5) (cos⁴(x)/4 + (2/3) cos⁶(x) - (1/9) cos⁸(x)) + C.The integral of the function can be expressed as (1/5) (sin⁻¹(cos(x)))⁵ - (1/5) (cos⁴(x)/4 + (2/3) cos⁶(x) - (1/9) cos⁸(x)) + C, where C is the constant of integration.

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Answer:

Positive

Step-by-step explanation:

It gose upwards

Answer:

The answer is = 3

Step-by-step explanation:

The given equation has only one root x=0.065. Hence, the total number of solutions is 1.

The equation sin 3x = 0.25 - x² is given and the number of solutions it has to be determined using Newton's method. Newton's method is an algorithm that is used to find the roots of a given function. I

n this method, we start with an initial guess and then we iteratively improve the guess until we converge to the root of the function.

Let's begin the solution for the equation sin 3x = 0.25 - x²:

Step 1: Find the derivatives of the given equation. sin 3x = 0.25 - x²

Differentiating the given equation on both sides w.r.t x, we get:3 cos 3x = -2x  

Now, we have the derivative of sin 3x.

Step 2: The Newton Raphson method is given by the formula:x 1 = x0 - f(x0)/f'(x0) where x1 and x0 are the successive approximation of the root and f(x0) is the function at x0 and f'(x0) is the derivative of the function at x0.

So, we will take x0= 0.1 (Initial guess) because this function has multiple roots and is an odd function. Hence, it has a root near x=0.1.

Step 3: We have f(x) = sin 3x - 0.25 + x² and f'(x) = 3 cos 3x + 2x'

We will find the next approximation x1 as follows: x1 = x0 - f(x0)/f'(x0)

x1 = 0.1 - [sin(3 * 0.1) - 0.25 + 0.1²]/[3 cos(3 * 0.1) + 2 * 0.1]

x1 = 0.0654

Step 4: We will repeat the above process using the value of x1 obtained in step 3. We will repeat it until the successive approximations become equal up to two decimal places.

We will continue the above process until we obtain the successive approximations that are equal up to two decimal places.

So, we get the root of the equation sin 3x = 0.25 - x² is x = 0.065 with the help of Newton's method.

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The number of ways to select a committee of four persons from a club consisting of six distinct men and seven distinct women, where the committee must include at least one woman, is given by the expression 7C1 × 6C3 + 7C2 × 6C2 + 7C3 × 6C1 + 7C4.

To determine the number of ways to form the committee, we can consider two cases: one with exactly one woman selected and another with more than one woman selected.

Case 1: Selecting exactly one woman: There are seven choices for selecting one woman and six choices for selecting three men from the remaining six men. The total number of combinations for this case is 7C1 ×6C3.

Case 2: Selecting more than one woman: We need to consider combinations with two women and two men, three women and one man, and all four women. The total number of combinations for this case is 7C2 × 6C2 + 7C3 × 6C1 + 7C4.

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Answer:

D

Step-by-step explanation:

10/2 + 5.2/2 = 7.6

Answer:

7.6cm

Step-by-step explanation:

Let's see - the midpoint of AB lies 10cm/2 from B and the midpoint of BC lies 5.2cm/2 from B in the other direction.

We can conclude that the midpoints are distant by

10cm/2 + 5.2cm/2 = 5cm + 2.6cm = 7.6cm

Answer:

She needs $60 more so she has to work 6 weeks to get that much.

Step-by-step explanation:

x = each week

y = total

Equation:

90 = 10x + 30

10x = 60

x = 6

Answer:

She needs 60 dollars, it would take her 6 weeks to reach this amount of money

Step-by-step explanation:

90 - 30 = 60 dollars

60 ÷ 10 = 6