Write the word sentence as an equation. Then solve.

10 more than a number c is 3.

Answer:

(1, -7) .................

The total amount accrued, principal plus interest, with compound interest on a principal of $2,000.00 at a rate of 8% per year compounded 1 times per year over 10 years is $4,317.85.

Given Data

Initial Amount = $2000

Annual interest rate = 8%

Time = 10 years

A = P + I where

P (principal) = $2,000.00

I (interest) = $2,317.85

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 2,000.00(1 + 0.08/1)(1)(10)

A = 2,000.00(1 + 0.08)(10)

A = $4,317.85

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Answer:

If 68.3% of Americans believe that some psychics can help solve murder cases, then the percentage of Americans who do not believe this is:

100% - 68.3% = 31.7%

Therefore, the probability of randomly selecting someone who does not believe that some psychics can help solve murder cases is 31.7%.

Step-by-step explanation:

Answer:

We can use the proportion:

48 pages / x = 80% / 100%

where x is the required length of the paper in pages.

First, we can simplify the right-hand side of the equation:

80% / 100% = 0.8

Next, we can solve for x by cross-multiplying:

48 pages / 0.8 = x

x = 60 pages

Therefore, the required length of the paper is 60 pages

Answer:

Step-by-step explanation:

Remark

The plan is to find the volume of one storage box. Then multiply by 6

Formula

1 storage box = 16.5 * 16.5 * 16.5

Solution

1 storage box = 16.5 * 16.5 * 16.5

1 storage box = 4492.125

6 storage boxes = 6 * 4492.125

6 storage boxes = 26952.75

Answer

Total Volume = 26952.75

No need to round at all. This already is at the nearest 1/100th

Answer:

C

Step-by-step explanation:

the nth term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

the first term a₁ from the table below n = 1, a₂ below n = 2 and so on

here a₁ = 100 and r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-50}{100}\) = - \(\frac{1}{2}\) , then

\(a_{n}\) = 100 \((-\frac{1}{2}) ^{n-1}\)

In this case, the experimental probability is D. 0.860

First, note that Experimental probability, also known as Empirical probability, is founded on real experiments and adequate documentation of events.

In the table we can see that he rolled the cube 1000 times, and he recorded that 140 of those times he rolled a 5.

Then, the probability of rolling a 5 will be equal to:

P1 = 140/1000 = 0.14

Now, the probabilty of NOT rolling a 5, is equal to the rest of the probabilities, this is:

P2 = 1 - 0.14 = 0.86

then the correct option is D

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Jimmy rolls a number cube multiple times and records the data in the table above. At the end of the experiment, he counts that he had rolled 140 fives. Find the experimental probability of not rolling a five, based in Jimmy’s experiment. Round the answer to the nearest thousandth.

A. 0.140

B. 0.167

C. 0.667

D. 0.860

The polynomial function in standard form that has the zeros listed. i and -i is  x² +1 = 0.

A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions.

The values of x that fulfil the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Calculation for the polynomial function-

The general two degree/quadratic equation is given by-

ax² + bx + c = 0

Where a ≠ 0

If the two roots of the equation are x1 and x2.

Then the relation between roots and coefficients of the polynomial are -

         x1 + x2 = (-b)/a

        x1.x2 = c/a

From the above two relation the general equation can be written as-

x² -(x1 - x2)x + x1.x2 = 0

Lets say x1 = i and x2 = -i

Substitute the values of x1 and x2 in the general equation

x² -(i - i)x + (i).(-i) = 0

x² - i ² = 0

x² + 1 = 0

Therefore, the polynomial function in standard form that has the zeros listed. i and -i is x² + 1 = 0.

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(D) the floor of a classroom is a perfect example of a line segment.

Therefore, (D) the floor of a classroom is a perfect example of a line segment.

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The correct form of the question is given below;
Which is an example of a line segment?

(A) the edge of a book

(B) the corner of a box

(C) a beam of light

(D) the floor of a classroom

Answer:

46 ÷ 5 3/4

Step-by-step explanation:

Expressions don't have equal signs.

Observing the given pattern in the equations :Equation 1: `a + x = 6`Equation 2: `2a + x = 8`Equation 3: `3a + x = 10`We notice that the constant term is incremented by 2 as we move from equation 1 to equation 2 and from equation 2 to equation .

Since the coefficient of `x` is constant in all equations, this implies that the value of `a` increases by `1` from equation 1 to equation 2 and increases by another `1` from equation 2 to equation 3.Hence, we can conclude that `a` increases by `1` for every increment of `2` in the constant term .Using this pattern, we can solve the equation for `a` as follows:To get from Equation 1 to Equation 2, the constant term increases by 2, and a increases by 1.So, we can express equation 2 in terms of equation 1 as follows :Equation 2 - Equation 1: `(2a + x) - (a + x) = 8 - 6`Simplifying the left-hand side of the equation: `2a - a + x - x = 2`Simplifying the equation further.

`a = 2`To get from Equation 2 to Equation 3, the constant term increases by 2, and a increases by 1.So, we can express equation 3 in terms of equation 2 as follows :Equation 3 - Equation 2: `(3a + x) - (2a + x) = 10 - 8`Simplifying the left-hand side of the equation: `3a - 2a + x - x = 2`Simplifying the equation further: `a = 2`Therefore, the solution of the equation for `a` is `a = 2`.

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As the sample size rises, the width of a 95% confidence interval for a sample proportion decreases.

If the sample size is four times greater than the initial sample size but the sample percentage remains constant, the breadth of the 95% confidence interval is reduced by around a factor of two.

This is due to the fact that the standard error, which defines the width of the confidence interval, is proportional to the sample size squared. When the sample size is multiplied by four, the square root of the sample size multiplies by two, resulting in a lower standard error and a smaller confidence range.

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Answer:

Step-by-step explanation:

To the 4th power means that all the items in the parenthesis is mulitplied 4 times

(9m)⁴

=9*9*9*9*m*m*m*m*m  or

= (9m)(9m)(9m)(9m)

Answer:

  11.4

Step-by-step explanation:

You want the distance between C(-5, 5) and D(4, -2).

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, the distance is computed to be ...

  d = √((4 -(-5))² +(-2 -5)²) = √(81 +49) = √130

  d ≈ 11.4

The length of CD is about 11.4 units.

__

Additional comment

The distance formula is an application of the Pythagorean theorem. It computes the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.

Answer:

23

Step-by-step explanation:

90cm that is the ans do you want the solution

Answer:

6cm

Step-by-step explanation:

answer is 6cm

The equation of the plane that contains the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 and is perpendicular to the plane x - y + z = 0 is x - y + z - 1 = 0.

To find the equation of the plane that contains the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 and is perpendicular to the plane x - y + z = 0, we can follow these steps:

Find the direction vector of the line of intersection of the given planes. To do this, we take the cross product of the normal vectors of the two planes.

Normal vector of plane 1: n₁ = (1, 1, 1)

Normal vector of plane 2: n₂ = (2, 3, 4)

Direction vector of the line of intersection: d = n₁ x n₂

Find a point that lies on the line of intersection. We can choose any point that satisfies both plane equations. Let's solve the system of equations:

x + y + z = 1

2x + 3y + 4z = 5

Solving the system, we find x = 1, y = -1, z = 1. So a point on the line of intersection is P(1, -1, 1).

Find the normal vector of the plane that is perpendicular to the plane x - y + z = 0. The coefficients of x, y, and z in the given plane equation serve as the normal vector. So, the normal vector of the perpendicular plane is n₃ = (1, -1, 1).

Use the point P(1, -1, 1) and the direction vector d = n₁ x n₂ to write the equation of the plane. The equation of a plane in point-normal form is given by:

(x - x₁, y - y₁, z - z₁) · n₃ = 0

Plugging in the values, we get:

(x - 1, y + 1, z - 1) · (1, -1, 1) = 0

Simplifying further, we have:

(x - 1) - (y + 1) + (z - 1) = 0

x - y + z - 1 = 0

Therefore, the equation of the plane that contains the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 and is perpendicular to the plane x - y + z = 0 is x - y + z - 1 = 0.

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The equilibrium points of the given system of equations are (x, y, z) = (-4, -5, 0) and (x, y, z) = (6, 7, 0). The stability of each equilibrium point will be discussed.

To find the equilibrium points, we set the derivatives equal to zero:

For x: 9 + x - 3y = 0

For y: (1 + x - y)y = 0

For z: z = 0

Solving the first equation, we get x = -4 + 3y. Substituting this into the second equation, we have (1 - 4 + 3y - y)y = 0. Simplifying, we obtain -3y^2 + 2y - 4 = 0. Solving this quadratic equation, we find y = -5 or y = 2/3.

For y = -5, substituting into the equation x = -4 + 3y, we get x = 6. Therefore, one equilibrium point is (x, y, z) = (6, -5, 0).

For y = 2/3, substituting into the equation x = -4 + 3y, we get x = -2/3. Therefore, another equilibrium point is (x, y, z) = (-2/3, 2/3, 0).

Now, let's analyze the stability of each equilibrium point. To do this, we calculate the Jacobian matrix J:

J = [∂f/∂x  ∂f/∂y  ∂f/∂z]

    [∂g/∂x  ∂g/∂y  ∂g/∂z]

Where f = 9 + x - 3y and g = (1 + x - y)y.

Evaluating J at each equilibrium point, we find:

J(6, -5, 0) = [1  -3  0]

                [1  -10  0]

J(-2/3, 2/3, 0) = [1  1/3  0]

                         [1  -4/3  0]

The eigenvalues of J(6, -5, 0) are -4 and -5, indicating a stable node.

The eigenvalues of J(-2/3, 2/3, 0) are approximately -0.717 and -2.283, indicating a saddle point.

Therefore, the equilibrium point (6, -5, 0) is stable, while the equilibrium point (-2/3, 2/3, 0) is a saddle point.

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The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

Explanation:

From the tape diagram, we can deduce the following;

*Total number of items = 87

*Number of subdivisions = 5 with one of them being a group of 39

Let's see which of the given stories that the tape diagram can represent;

A) Total number of first graders = 87

Students picked up = 39

Number of groups the remaining students were divided into = 4

We can see from the above that the tape diagram can represent this story

B) Number of children at the show = 87

Number of adults at the show = 39

Total number of people at the show = 87 + 39 = 126

We can see from the above that the tape diagram can not represent this story

C) Number of packs of pencils Lin bought = 87

Number of packs she gave to her teacher = 39

She then shared the remaining packs between herself and 3 friends

We can see from the above that the tape diagram can represent this story

D) Total amount Diego's family spent to a fair = $87

Amount spent on dinner = $39

They spent the remaining spent on 4 tickets

We can see from the above that the tape diagram can represent this story

E) Number of packs of paper clips Adre bought = 4

Number of paper clips in each = 39

Total number of paper clips bought = 39 x 4 = 156

We can see from the above that the tape diagram can not represent this story

Answer: 4

Step-by-step explanation: 10-6=4

14-10=4

The solution of the inequality 5m + 1 ≤ 4 is less than or equal to 0.80.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

5m + 1 ≤ 4

Simplify the equation, then we have

5m + 1 ≤ 4

5m ≤ 4

m ≤ 4 / 5

m ≤ 0.8

The solution of the inequality 5m + 1 ≤ 4 is less than or equal to 0.80.

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The linear equation that gives the rule for this table is: y = -7x - 13. Let's use the first data point.

To write the linear equation that gives the rule for the given table: x y; 2 -27; 3 -34; 4 -41; 5 -48. We can observe that as x increases by 1, y decreases by 7. This indicates a constant rate of change of -7.  Using this information, we can write the linear equation as: y = -7x + b. To find the value of b, we can substitute the values of x and y from any data point in the table.

Let's use the first data point (2, -27): -27 = -7(2) + b. Solving for b, we get: b = -27 + 14; b = -13. Therefore, the linear equation that gives the rule for this table is: y = -7x - 13.

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Answer:

m<QRS=48°

m<RSQ=69°

m<RQS=63°

Step-by-step explanation:

Since we know that the measures of the angles of any triangle is 180°, we can form this equation: 7a-1+10a-1+9a=180°

Then, we can use simple algebra to solve for a and plug in that value into the equations that the degrees represent to get our angle measures.

7a-1+10a-1+9a=180°

26a-2=180°

26a=182°

a=7

Now, plug in that value of a and you have your anlage measures!! Hope this helps!! :)

Answer:

The sum of 10 and  a subtraction of 4 from 6.  

Step-by-step explanation:

I know some math. Hope this helps! :D

its 8 because you subtract first and then you add 10

Answer:

The expanded form of 1.2*10^9 is 1400000000

I'm not very sure what you mean but I have found two solutions.

Solution No.1:

1400000000 - 7000 = 1399993000

Solution No.2:

Let's say the variable is "x"

7000 * x = 1400000000

x = 200000

Hope this helped! :)