A line shape like a trapezoid has an area of 337. 5ft^2 if the length of the bases are 25 fr and 20 ft then the perpendicular distance between bases would be

The magnitude of the acceleration is approximately -0.267 m/s², and the car does not hit the deer.

To find the magnitude of acceleration, we need to consider the forces acting on the car. The gravitational force component parallel to the incline is given by \(\( F_g = m \cdot g \cdot \sin(10^\circ) \)\), where \(\( m \)\) is the mass of the car and \(\( g \)\) is the acceleration due to gravity. The frictional force opposing the motion is given by \(\( F_f = m \cdot g \cdot \cos(10^\circ) \cdot \mu_k \)\), where \(\( \mu_k \)\) is the coefficient of kinetic friction.

The net force acting on the car is the difference between the gravitational force and the frictional force: \(\( F_{\text{net}} = F_g - F_f \)\).

Using Newton's second law, \(\( F_{\text{net}} = m \cdot a \)\), where \(\( a \)\) is the acceleration. We can solve for \(\( a \)\) by rearranging the equation: \(\( a = \frac{F_{\text{net}}}{m} \)\).

Substituting the given values and calculating the magnitude of acceleration:

\(\[ a = \frac{m \cdot g \cdot \sin(10^\circ) - m \cdot g \cdot \cos(10^\circ) \cdot \mu_k}{m} \\\)

\(\quad = g \cdot (\sin(10^\circ) - \cos(10^\circ) \cdot \mu_k) \]\)

Now, let's calculate the value of the acceleration. We are given that the speed of the car is 25 mph, which is equivalent to \(\( 25 \times \frac{1609}{3600} \)\) m/s.

Using \(\( g = 9.8 \, \text{m/s}^2 \)\) and \(\( \mu_k = 0.4 \)\), we have:

\(\[ a = 9.8 \cdot (\sin(10^\circ) - \cos(10^\circ) \cdot 0.4) \approx -0.267 \, \text{m/s}^2 \]\)

The negative sign indicates that the acceleration is in the opposite direction of the car's motion.

To determine if the car hits the deer, we need to compare the stopping distance of the car to the distance to the deer. The stopping distance can be calculated using the equation: \(\( d = \frac{v^2}{2 \cdot a} \)\), where \(\( v \)\) is the initial velocity and \(\( a \)\) is the acceleration.

Substituting the given values, we have:

\(\[ d = \frac{(25 \times \frac{1609}{3600})^2}{2 \cdot (-0.267)} \approx 596 \, \text{m} \]\)

Since the stopping distance (596 m) is greater than the distance to the deer (25 m), the car does not hit the deer.

Therefore, the magnitude of acceleration is approximately \(\( -0.267 \, \text{m/s}^2 \)\) and the car does not hit the deer.

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7. 51 customers said oatmeal raisin or peanut butter.

8. 42 customers said oatmeal raisin or peanut butter was their favorite cookie.

7. From the given circle graph, it can be seen that

chocolate chip is 14%

hence we can say that

14% of 150 = 0.14 x 150 = 21 customers

51 customers said oatmeal raisin or peanut butter

8. The oatmeal raisin or peanut butter

20% + 8% = 28%

28% of the customers said oatmeal raisin or peanut butter was their favorite cookie  which is equivalent to

0.28 x 150 = 42 customers

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The students who read newspapers is 30, and the read story books is 90.

Let number of students read newspapers as N and story books as S.

We have

Out of 110 students, 10 read neither newspaper nor story book.

This means that these 10 students are not included in either N or S.

As, students who read story books is three times read newspapers. then, S = 3N.

So, the total number of students who either read newspapers or story books is given by:

= 110 - 10

= 100

and, the total number of students who either read newspapers or story books is given by:

N + S - 20 = 100

Substituting S = 3N, we have:

N + 3N - 20 = 100

4N - 20 = 100

4N = 120

N = 30

Now, we can calculate the number of students who read story books:

S = 3N = 3 c 30 = 90

Therefore, the students who read newspapers is 30, and the read story books is 90.

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The number that satisfies the given equation is 2.

Let's solve the equation step by step.

Let's assume the number is represented by "x".

According to the given information, the equation can be written as:

3 + 1/x = 7/x

To simplify the equation, we can multiply both sides of the equation by "x" to eliminate the denominators:

3x + 1 = 7

Next, we can isolate the variable by subtracting 1 from both sides:

3x = 7 - 1

3x = 6

Finally, we can solve for "x" by dividing both sides by 3:

x = 6/3

x = 2

Therefore, the number is 2.

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Answer:

2.2

Step-by-step explanation:

When the level of significance is 0.07, the corresponding confidence level is 93%.

The level of significance (α) in statistical hypothesis testing represents the probability of rejecting the null hypothesis when it is actually true. In contrast, the confidence level represents the degree of certainty or reliability we have in the estimated results from a statistical analysis.

The confidence level is calculated as the complement of the level of significance, subtracted from 1. In this case, if the level of significance is 0.07, we subtract it from 1 to find the confidence level:

Confidence level = 1 - level of significance

Confidence level = 1 - 0.07

Confidence level = 0.93 or 93%

Therefore, when the level of significance is 0.07, the corresponding confidence level is 93%. This means that we can be 93% confident that the estimated results from a statistical analysis will fall within the desired range, while allowing for a 7% chance of Type I error (rejecting the null hypothesis when it is true).

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The price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

Given:

The mean, m = $17000,

The standard deviation, σ = $500

Calculate the 3rd standard deviation as shown below,

3rd standard deviation  = mean + 3 × standard deviation

3rd standard deviation = 17000 + 3 × 500

3rd standard deviation = 17000 + 1500

3rd standard deviation = $18500

Therefore, the price that is 3rd standard above the mean, if the mean is $10000  and the standard deviation is $500 is $18500.

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Answer:

See below

Step-by-step explanation:

f(x - 1) is the translation of f(x) one unit right.

So the graph is exactly same shape but shifted right one unit.

f(x) has vertex (-1, 2)

The function y = f(-x) + 2 will have the vertex changed as per rule:

So the new vertex is:

Answer:

On Wednesday evening Sonto spent 30 minutes doing homework, 45 minutes doing housework, 60 minutes visiting friends and 90 minutes watching television. Write this down the information as a ratio​

Step-by-step explanation:

Total amount of time = 225 minutes

2/15 Homework

1/5 Housework

4/15 Visiting friends

2/5 Watching TV

Whole number ratio

2 : 3 : 4 : 6

Answer:

10/1 = X

Cross multiply

X = 10

the 45

Step-by-step explanation:

679

Answer:

54/11 (or) 4 10/11

Step-by-step explanation:

Let's solve the problem,

→ 18 ÷ 3 2/3

→ 18 ÷ (11/3)

→ 18 × (3/11)

→ 54/11 = 4 10/11

Hence, the answer is 54/11.

Answer:

300

Step-by-step explanation:

5 or more raise the score 4 or less let it rest basically 5 or more up 4 or less down

Answer:

60 degrees

Step-by-step explanation:

First of all, we have to set up an equation to solve this. The angles of a triangle add up to 180 degrees. We need to find the internal angle of C, which would be 180-(10x-45).

For our equation, we can set 3x+4x+[180-(10x-45)] equal to 180.

Add like terms:

7x+[180-(10x-45)] = 180

Distribute:

7x+180-10x+45 = 180

Add like terms once again:

-3x+225 = 180

Subtract 225 on both sides:

-3x = -45

Divide by -3 on both sides:

x = 15

Plug in 15 for x in the value 4x:

<B = 60 degrees

Answer:

  (b)  domain: {-2, 0, 2}, range: {-1, 0, 1}

Step-by-step explanation:

For the function defined by the table ...

  \(\begin{array}{|cccc|}\cline{1-4}x&-2&0&2\\\cline{1-4}y&-1&0&1\\\cline{1-4}\end{array}\)

we want the function's domain and range.

__

The domain is the list of x-values for which the function is defined. Here, that list is ...

  domain = {-2, 0, 2}

__

The range is the list of y-values the function produces. Here, that list is ...

  range = {-1, 0, 1}

_____

The domain and range sets are most conveniently listed in order, with duplicates removed.

Answer:

7 1/2 ÷ 1 1/2

make them improper fractions;

15/2 ÷ 3/2

make 3/2 a reciprocal(basically flipping the fraction upside down)

15/2 ÷ 2/3

and multiply across;

15/2 x 2/3 = 30/6 which simplifies to 5 bags of flour.

The statement A∧(B∨C)↔[(A∧B)∨(A∧C)] is always true.

This can be demonstrated by constructing a truth table for all possible combinations of truth values for A, B, and C. In every row of the truth table, the truth values of the two sides of the biconditional (↔) are always the same, indicating that the statement is always true regardless of the values of A, B, and C.

what is biconditional?

In logic and mathematics, a biconditional, also known as a double implication, is a logical connective that represents a statement of equivalence between two propositions. It is denoted by the symbol "↔" or "⇔".

The biconditional "P ↔ Q" is true when both P and Q have the same truth value. It means that P is true if and only if Q is true. In other words, P and Q are logically equivalent, and their truth values always match.

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Answer:

1. (2.2, -1.35) and (2.2, -1.4)

2. y = 8x - 7

3. infinite number of solutions

4. (2.2,-1.4) (2.2,-1.35)

5. 6

6. (1.33,1)

Step-by-step explanation:

The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.

From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.

So, Minimum Value = 1.0

Maximum Value = 11.2

Range = Maximum Value - Minimum Value

                  = 11.2 - 1.0

                     = 10.2

Therefore, the range of the given data is 10.2.

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Answer:

y = 4(3)^x

Step-by-step explanation:

Here, we want to write the exponential equation

From the question, we have the equation tripling in x value every year and the original amount is 4

The exponential equation is of the form;

y = a(b)^n

In this case;

a = 4 , b = 3 and n = x

So we have the equation as;

y = 4(3)^x

Using simple interest, it is found that the interest rate was of 3%.

The amount of simple interest generated after t years is given by:

\(I = Prt\)

In which:

In this problem:

Then, we solve the equation of simple interest for r.

\(I = Prt\)

\(100.8 = 480(7)r\)

\(r = \frac{100.8}{480(7)}\)

\(r = 0.03\)

The interest rate was of 3%.

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Step-by-step explanation:

as, the traingle is equilateral triangle Which means it's all sides are equal

therefore, VT and BT are x

→ BV = VT = BT = x

hope this answer helps you dear take care!

The relative risk of stroke in hyper .tensive as compared to non-hypertensive person formula is PP (exposed)/ PP (unexposed).

There are foremost causes of stroke: a blocked artery (ischemic stroke) or leaking or bursting of a blood vessel (hemorrhagic stroke). some people may additionally have best a transient disruption of blood glide to the mind, known as a brief ischemic attack (TIA), that does not purpose lasting symptoms.

Low-depth physical games have a lower hazard of harm and are endorsed for human beings with different fitness troubles. some low-depth sports are: walking. Gardening and other backyard work

life-style factors that growth your hazard of stroke consist of high blood stress, smoking, diabetes, excessive blood cholesterol levels, heavy ingesting, high salt and excessive fat food regimen and lack of exercise.

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The Y-intercept, b₀ = 14, implies that when the value of X is 0, the mean value of Y is 14.

The equation of a straight line can be represented by the equation y=mx+c where m is the slope of the line and c is the y-intercept. y is the dependent variable and x is the independent variable.

The given equation is:

\(Y_i = 14 - 0.2X_i\)

Y-intercept is the value of y when x=0. The y-intercept is 14.

Therefore, option d: The Y-intercept,  b₀ = 14, implies that when the value of X is 0, the mean value of Y is 14 is the correct answer.

Option a: The Y-intercept, b₀ = -0.2, implies that when the value of X is 0, the mean value of Y is -0.2 is wrong because the slope cannot be negative.

Option b: The Y-intercept, b₀ = 14, implies that the average value of Y is 14 is wrong because the y-intercept does not indicate the average value of y. It only represents the value of y when x=0.

Option c: The Y-intercept, b₀ = 14, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 14 units is wrong because the slope is negative (-0.2) and the value of y decreases as the value of x increases.

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For the moving platform shaped in parallelogram, the correct number in each box is

The result is obtained by using the properties of angles in parallelogram.

The properties of angles in parallelogram are:

There are 2 pairs of sides of parallelogram. A pair of sides are parallel to each other and have the same length.

In the picture, we have

Find x, m∠A, AB, and BC!

m∠D and m∠C are consecutive angles. So,

35° + (4x + 5) = 180°

35° + (4x + 5)° = 180°

40° + 4x = 180°

4x = 180° - 40°

4x = 140°

x = 140°/4

x = 35°

m∠A and m∠C are the opposite angles. So, they are equal.

m∠A = m∠C

m∠A = (4x + 5)°

m∠A = (4(35) + 5)°

m∠A = 145°

AB is parallel to DC. So,

AB = DC = 32 ft

BC is parallel to AD. So,

BC = AD = 14 ft

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A circle is a curve sketched out by a point moving in a plane. The area of the sector PQR is 41.346 units².

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

Given the radius of the circle is 8 units, while the angle of the sector is 74°. Therefore, the area of the sector is,

Area of the sector = π×R²×(74/360)

                              = π × 8² × 0.20556

                              = 41.346 units²

Hence, the area of the sector PQR is 41.346 units².

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