Lisa puts $8,000 in an account that earns 12% simple annual interest. If she leaves her money in the account for 4 years, how much interest will she earn?

Step-by-step explanation:

x= 180-109 = 71°

y= 360-81-71-100= 108

The Average Speed of car for the round trip is 346.28 km/ hr.

Average Speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.

If a  car travels a distance d at rate r₁ and return the same distance at rate r₂, then,

Average Speed =  total distance ÷ total time

                          = 2d ÷ d/r₁ + d/r₂

                          = 2d ÷ r₂d + r₁d / r₁r₂

                          = 2r₁r₂ / r₁ +r₂

∴ x = 2× 3030×4040/ 3030 +4040

     = 2448240 ÷ 707

     = 346.28 km/hr

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Answer:

935 yards

Step-by-step explanation:

If she runs 85 yards at each practice you would multiply it by the amount of practices. So 85x11

Answer:

Step-by-step explanation:

1. Imagine a triangle with base side 36 feet and Kate at the right with the angle of elevation, 24 degrees. We can use tangent:

tan 24 = o/a ; tan(24) = o/36 ; 36(tan(24)) = o ; o = 16 feet

This is how tall the screen is.

2. We do a similar operation:

tan(74) = o/a ; tan(74) = 555/a ; a = 555/tan(74) ; a = 159.1 feet

Hope this helps!

The cost for children meal is $14 and the cost for adult meal is $40.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Let cost of adult meal = a

Let cost of child meal = c

Lorenzo plans to have 98 adults and 77 children attend, so the total projected cost of her meals is $4998.This will be:

98a + 77c = 4998 ...... (1)

Ruth has 71 adults and 91 children on her guest list, so he will pay the caterer $4114. This will be;

71a + 91c = 4114 ......    (2)

Multiply (1) by 71 and (2) by 98

6958a + 5467c = 354858      (3)

6958a + 8918c = 403172         (4)

subtract (3) from (4)

3451 c = 48314

c = 14

The cost of children meal is $14.

From equation (1),

98a + 77c = 4998

98a + 77(14) = 4998

98a + 1078 = 4998

Collect like terms

98a = 4998 - 1078

98a = 3920

a = 40

Adult meals is $40.

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Answer:

see below

Step-by-step explanation:

5|x| + 3 < 18

Subtract 3 from each side

5|x| + 3-3 < 18-3

5|x| < 15

Divide by 5

5|x| /5 < 15/5

|x|  < 3

There are  two solutions for an absolute value, one positive and one negative ( the negative flips the inequality)

x <3  and  x > -3

Answer:5|x| + 3 < 18

Step-by-step explanation:

Answer:

should be 17

Step-by-step explanation:

By analyzing the bases of the exponential equations, we can see that:

Exponential decay              Exponential growth.

h(x) = 1.02*(0.06)^2              h(x) = 0.98*(3)^x

h(x) = 4*(0.74)^x                    h(x) = 9*(1.3)^x

A general exponential function is written as:

f(x) = A*(b)^x

Where A is the initial value, b is the base, and x is the variable.

The first one is:

h(x) = 0.98*(3)^x

The base is b = 3, so this is an exponential growth.

The second one is:

h(x) = 1.02*(0.06)^2

The base is b = 0.06, smaller than 1, then this is an exponential decay.

The third one is:

h(x) = 4*(0.74)^x

The base is b = 0.74, again this is smaller than 1, so we have an exponential decay.

The last one is:

h(x) = 9*(1.3)^x

The base is b = 1.3 > 1, then we have an exponential growth.

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Answer: x=4

Step-by-step explanation:

6x + 10 = 5x + 14

x + 10 = 14

x = 4

Answer:

48°

Step-by-step explanation:

1) The sum of the interior of any triangle is 180°. a + b + c = 180°. We need to find the value of x first before finding the angle F.

2) Substitute the values into a + b + c = 180, where \(a=6x-4\), \(b =5x-7\), \(c=8x-18\).

Hence,

\(6x-4+5x-7+8x-18=180\\19x-29=180\\19x=180+29\\19x=209\\x=\frac{209}{19} \\x=11\)

3) Find the angle of F by substituting 11 into x.

\(=5(11)-7\\=55-7\\=48\)

Therefore, angle F has a measure of 48°.

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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The equations are dependent and represent the same line on the coordinate plane, its has more than one solution.

Given the system of equation in the question:

y = x - 3

3y - 3x = -9

To determine the number of solutions for the given system of equations, let's analyze the equations:

y = x - 3 --------(1)

3y - 3x = -9 ---(2)

Simplify equation (2) by dividing both sides by 3:

3y/3 - 3x/3 = -9/3

y - x = -3

Now, we have the following system of equations:

y = x - 3

y - x = -3

To solve this system, we can use the method of substitution.

From equation (2), we can express y in terms of x:

y = x - 3

Substituting this expression for y into equation (1):

x - 3 = x - 3

Since two equations are equivalent, this means that the system has infinitely many solutions.

Option D) More than 1 solution is the correct answer.

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Answer:

4a LBS

Step-by-step explanation: If you make the unknown x, then your expression will be 0.25x=a, or 1/4x=a. If you multiply both sides by 4, then you will find that the expression is x=4a. Therefore, your answer is 4a LBS. Good Luck!

The value of the number is 4a

Data;

This is the ratio of a number to the entire number and multiplied by 100.

\(25 \% = \frac{a}{x}\)

We can further elaborate this

\(\frac{25}{100} = \frac{a}{x} \\ \frac{1}{4} = \frac{a}{x}\\ x = 4a\)

The value of the number is 4a

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Step-by-step explanation:

(2a+3b)(4a²-6ab+9b²

(2a+3b){(2a)²-2a×3b+(3b)²}

Because (a³+b³)=(a+b)(a²-ab+b²)

Therefore,

(2a+3b){(2a)²-2a×3b+(3b)²}

=(2a)³+(3b)³

By substituting the values , we get

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

In statistics, hypothesis testing is one of the most important techniques used to test claims or statements regarding population parameters. The hypothesis testing process consists of six steps, including state the null and alternative hypotheses.

Null Hypothesis, H0: p ≤ 0.65 Alternative Hypothesis, Ha: p > 0.65 Where p is the proportion of computer chips that do not fail in the first 1000 hours of their use. Now we have to check whether there is sufficient evidence at the 0.01 level to support the company's claim or not. For this, we use the following formula to compute the z-score for the sample proportion.

\($$z=\frac{p-_0}{\sqrt{_0(1−_0)/}}$$\)  where

p0 = 0.65 (assumed under null hypothesis)

p = 0.69 (sample proportion)

n = 900 (sample size) Now, we have,

\($$z=\frac{0.69-0.65}{\sqrt{0.65(1−0.65)/900}}$$ $$\implies z=\frac{0.04}{0.0156}=2.564$$\)

The null and alternative hypotheses for the given scenario are H0: p ≤ 0.65 and Ha: p > 0.65. At the 0.01 level, there is sufficient evidence to support the company's claim that more than 65% of computer chips do not fail in the first 1000 hours of their use.

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To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.

The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.

For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.

To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.

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The point in the first quadrant at which the line intersects the circle is; ; (√5, 2√5+1).

Since the equation of a circle whose radius is 5 and center is; (0, 1) is as follows;

(x-0)² + (y-1)² = 5².

Hence, since the line, y = 2x +1, intersects the circle in the first quadrant;

By substitution, we have;

x² + (2x+1-1)² = 25

5x² = 25

x² = 5.

Hence, x = ±√5, more specifically, x = √5 in the first quadrant and hence, y = 2√5 +1.

The required point is therefore; (√5, 2√5+1).

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Answer:

228

Step-by-step explanation:

Upper Control Limit (UCL) for R chart = D4 x Rbar = 2.282 x 0.347 = 0.792 and Lower Control Limit (LCL) for R chart = D3 x Rbar = 0 x 0.347 = 0.

To determine the trial central line and control limits for the X and R control charts, we need to first calculate the average and range of each subgroup.
Average (Xbar):
Subgroup 1: 20.35
Subgroup 2: 20.40
Subgroup 3: 20.36
Subgroup 4: 20.65
Subgroup 5: 20.20
Subgroup 6: 20.40
Subgroup 7: 20.43
Subgroup 8: 20.37
Subgroup 9: 20.48
Subgroup 10: 20.42
Subgroup 11: 20.39
Subgroup 12: 20.38
Subgroup 13: 20.40
Subgroup 14: 20.41
Subgroup 15: 20.45
Subgroup 16: 20.34
Subgroup 17: 20.36
Subgroup 18: 20.42
Subgroup 19: 20.50
Subgroup 20: 20.31
Subgroup 21: 20.39
Subgroup 22: 20.39
Subgroup 23: 20.40
Subgroup 24: 20.41
Subgroup 25: 20.40

Average (Xbar) = (20.35 + 20.40 + 20.36 + 20.65 + 20.20 + 20.40 + 20.43 + 20.37 + 20.48 + 20.42 + 20.39 + 20.38 + 20.40 + 20.41 + 20.45 + 20.34 + 20.36 + 20.42 + 20.50 + 20.31 + 20.39 + 20.39 + 20.40 + 20.41 + 20.40)/25 = 20.408
Range (R):
Subgroup 1: 0.34
Subgroup 2: 0.36
Subgroup 3: 0.32
Subgroup 4: 0.36
Subgroup 5: 0.36
Subgroup 6: 0.35
Subgroup 7: 0.31
Subgroup 8: 0.34
Subgroup 9: 0.30
Subgroup 10: 0.37
Subgroup 11: 0.29
Subgroup 12: 0.30
Subgroup 13: 0.33
Subgroup 14: 0.36
Subgroup 15: 0.34
Subgroup 16: 0.36
Subgroup 17: 0.37
Subgroup 18: 0.73
Subgroup 19: 0.38
Subgroup 20: 0.35
Subgroup 21: 0.33
Subgroup 22: 0.33
Subgroup 23: 0.30
Subgroup 24: 0.34
Subgroup 25: 0.30

Range (R) = max(Range of each subgroup) - min(Range of each subgroup) = 0.73 - 0.29 = 0.44
Using these values, we can now calculate the trial central line and control limits:
Central line (CL) for X chart = Xbar = 20.408
Upper Control Limit (UCL) for X chart = CL + (A2 x Rbar) = 20.408 + (0.577 x 0.44) = 20.672
Lower Control Limit (LCL) for X chart = CL - (A2 x Rbar) = 20.408 - (0.577 x 0.44) = 20.144
Central line (CL) for R chart = Rbar = (0.34 + 0.36 + 0.32 + 0.36 + 0.36 + 0.35 + 0.31 + 0.34 + 0.30 + 0.37 + 0.29 + 0.30 + 0.33 + 0.36 + 0.34 + 0.36 + 0.37 + 0.73 + 0.38 + 0.35 + 0.33 + 0.33 + 0.30 + 0.34 + 0.30)/25 = 0.347
Upper Control Limit (UCL) for R chart = D4 x Rbar = 2.282 x 0.347 = 0.792
Lower Control Limit (LCL) for R chart = D3 x Rbar = 0 x 0.347 = 0
If any points fall outside of these control limits, it suggests that the process is out of control and requires investigation for assignable causes. Upon investigating, any assignable causes should be removed and the control chart revised accordingly.

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Answer:

Step-by-step explanation:

To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.

To use this formula, we first need to find the slope of the line that passes through the two given points (-4, -2) and (-6, -5). The slope, denoted by m, is given by the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-4, -2) and (x2, y2) = (-6, -5). Substituting these values, we get:

m = (-5 - (-2)) / (-6 - (-4))

= (-5 + 2) / (-6 + 4)

= -3 / -2

= 3/2

So, the slope of the line is 3/2.

Now, we can choose either of the two given points and use it with the slope to write the equation of the line. Let's use the first point, (-4, -2). Substituting the values of x1, y1, and m in the point-slope formula, we get:

y - (-2) = (3/2)(x - (-4))

Simplifying the right side of the equation, we get:

y + 2 = (3/2)(x + 4)

Expanding the right side, we get:

y + 2 = (3/2)x + 6

Subtracting 2 from both sides, we get:

y = (3/2)x + 4

So, the equation of the line that passes through the points (-4, -2) and (-6, -5) is:

y = (3/2)x + 4

An older household with an annual income of $53,000 typically spends approximately 30% to 35% of their income on housing, which amounts to roughly $15,900 to $18,550 per year.

The recommended guideline for housing expenses suggests that individuals or households should spend no more than 30% of their income on housing costs. However, older households often have different financial considerations and may allocate a larger portion of their income towards housing. Based on the provided annual income of $53,000, we can estimate the housing expenses for an older household in the age range of 65-74.

To calculate the approximate amount spent on housing, we can use the range of 30% to 35% of the annual income. Multiplying $53,000 by 0.30 gives us $15,900, which represents the lower end of the estimated housing expenses. Similarly, multiplying $53,000 by 0.35 gives us $18,550, which represents the higher end of the estimate. Therefore, an older household with an annual income of $53,000 is likely to spend approximately $15,900 to $18,550 per year on housing. It's important to note that individual circumstances, such as location, housing type, and personal preferences, can vary, leading to different spending patterns.

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Answer:

b=(28+a²)^½

Step-by-step explanation:

but i couldnt find the numerical value of b since the value of a wasn't given

Answer:

3/10 liters more

Step-by-step explanation:

8/10 - 5/10 = 3/10

Answer:

The argument for the square root cannot be negative, nor can the denominator expression be zero. Hence the square root argument must be strictly positive, i.e. .

As an interval, the domain is

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

Step-by-step explanation:

By looking at the differential equation y' = -(1/6)y^2, we can deduce that the solution will involve a decreasing function due to the negative sign and the squared term.

The equation indicates that the rate of change of y is proportional to the square of y itself.

Identify the form of the differential equation: The equation y' = -(1/6)y^2 is a first-order ordinary differential equation. It is separable since it can be rearranged to isolate y and y' on opposite sides of the equation.

Analyze the right-hand side of the equation: The negative sign in front of the term (1/6)y^2 implies that the derivative y' is negatively related to y^2. This indicates that the rate of change of y decreases as the value of y increases.

Determine the behavior of the solution: Based on the differential equation, we can infer that the solution y(x) will be a decreasing function. As y increases, the rate of change (y') decreases, suggesting that the function approaches a steady state or an asymptote.

Consider the initial conditions: To find the specific solution, initial conditions or boundary conditions must be given. The solution will depend on these conditions.

In summary, the differential equation y' = -(1/6)y^2 suggests that the solution y(x) will be a decreasing function. The negative sign and the squared term indicate that the rate of change decreases as y increases. The exact solution can be determined by considering the initial or boundary conditions.

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Answer:

To find the exterior angle of any polygon, just construct a line following one of the sides, and measure the angle.

Step-by-step explanation:

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