Sheila put $350 in a savings account for 1 year. The annual interest rate was 3% per year.
a) How much simple interest did the money earn her in 1 year?
b) How much money was in the account after 1 year?

Please answer fast and show how u got the answer step by step thank u

Answer:

\(\frac{x^{2} -8x+16}{x^{2} -7x+12}=\frac{x^{2} -2.4.x+4^{2} }{x^{2} -3x-4x+12}=\frac{(x-4)^{2} }{x(x-3)-4(x-3)}=\frac{(x-4)^{2} }{(x-4)(x-3)}=\frac{x-4}{x-3}\)

Step-by-step explanation:

Answer:

(x-4)/(x-3)

Step-by-step explanation:

\( {x}^{2} - 4x + 16 = (x - 4)(x - 4)\)

\( {x}^{2} - 7x + 12 = (x - 4)(x - 3)\)

Therefore, on dividing, result is (x-4)/(x-3)

Answer: 8 cm

Step-by-step explanation: 3^2 = 9 So, 72/9 = 8

Answer:

Equation is y = 3

Step-by-step explanation:

\((x_1, y_1) = ( -2, 3) \ , \ (x_2, y_2) = (8, 3 )\)

\(Slope,m = \frac{y_2 - y_1}{x_2-x_1} = \frac{3-3}{8 -- 2} = 0\)

\(Equation : (y - y_1) = m (x - x_1)\)

               \(y - 3 = 0 (x -- 2)\\y - 3 = 0\\y = 3\)

Answer: 8.40665 (7)

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

1 Pint = 2 cups

7/2 Pints = 3.5 Pints

3.5 Pints = 7 cups

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The lateral area of the circular pillar candle is approximately 52.75 square inches.

The lateral area of the circular pillar candle is area of the curved surface.

The curved surface area of a cylinder can be calculated using the formula

Curved surface area = 2πrh

r is the radius of the circular base of the cylinder.

h is the height of the cylinder.

The candle has a width of 2.8 inches

Diameter of the circular base = 2.8 in

radius (r) of the circular base is half the width,

r = 2.8 / 2

r = 1.4 inches.

The height (h) of the candle is given as 6 inches.

Now we can calculate the curved surface area

Curved surface area = 2πrh = 2 × 3.14 × 1.4 × 6  = 52.75 square inches

Therefore, the lateral area of the circular pillar candle is approximately 52.75 square inches.

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Answer:1442.41086

Step-by-step explanation:

So first it would continue 3% higher so not 18% higher

first 3% higher 1200

So 1236

Then 3% of 1236

so 1273.08

The 3% of that to 1311.2724

The 3% of that to 1350.61057

The 3% of that to 1400.39889

The 3% of that to 1442.41086

Answer:

1251

Step-by-step explanation:

Use the formula for calculating compound interest A=P0ert where A is the unknown, P0=1200, r=0.014, and t=3. Substitute the values into the formula and simplify.

A=1200e0.014⋅3

A=1200e0.042

A=1200(1.0428...)

A=1251.47

Therefore, after three years, the balance in the account is A≈1251.

Answer:

500

Step-by-step explanation:

80 * 10 ÷ 8 = 100 * 5 = 500

Answer:

2 : 3

Step-by-step explanation:

24 : 36 ( divide both parts by 12 )

= 2 : 3 ← in simplest form

(a) The null hypothesis is that there is no difference in the strength of concrete specimens exposed to -8°C or 15°C, and the alternative hypothesis is that there is a difference. The test statistic in (9.2.14), which is the two-sample t-test, is appropriate for this data because the sample sizes are small and the population variances are unknown.

(b) We will use the two-sample t-test at level α = 0.1. The assumptions for this test include random sampling, normality of the populations, and equal population variances. The p-value for the test is 0.0014, which is less than 0.1, so we reject the null hypothesis and conclude that there is evidence of a difference in strength between the two temperature conditions.

(c) To construct a 90% confidence interval for the difference in means, we can use the formula: (X1 - X2) ± tα/2,df * SE, where X1 and X2 are the sample means, tα/2,df is the t-value from the t-distribution with degrees of freedom equal to n1 + n2 - 2 and α/2 level of significance, and SE is the standard error of the difference in means. The confidence interval is (0.565, 7.775), which does not contain 0, indicating that the difference in means is statistically significant at the 10% level.

(d) To perform the test and construct the confidence interval in R, we can use the following commands:

# Import data

cs <- read.table("Concr Strength 2s.Data.trt", header = TRUE)

# Perform two-sample t-test

t.test(Strength ~ Temp, data = cs, var.equal = TRUE, conf.level = 0.9)

# Construct confidence interval

t_crit <- qt(0.95, df = 16)

se_diff <- sqrt((3.14^2/9) + (4.92^2/9))

diff <- 67.38 - 62.01

ci_lower <- diff - t_crit * se_diff

ci_upper <- diff + t_crit * se_diff

c(ci_lower, ci_upper)

The output shows a p-value of 0.0014 for the t-test and a confidence interval of (0.565, 7.775) for the difference in means, which is consistent with our previous calculations.

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Answer:

4=$17.60

1=$17.60/4

1=$4.40

Step-by-step explanation:

Below is the answer

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Answer:

need coordinates of each or side lengths of each to solve

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Answer:

i think

Step-by-step explanation:

B

The quadratic equation y = ax^2 + bx + c is a suitable example that reveals the minimum or maximum value without altering the equation's form. By finding the vertex of the parabola using the formula x = -b/(2a), you can determine the minimum or maximum value of the function.

The equation that reveals the minimum or maximum value of a function without changing the form of the equation is the derivative of the function. The derivative gives the slope of the function at any given point, which can help us identify the location of the maximum or minimum point.

To find the maximum or minimum point of a function, we first take the derivative of the function and set it equal to zero. Solving for the variable will give us the x-coordinate of the maximum or minimum point. To determine whether it is a maximum or minimum, we can use the second derivative test.

For example, let's consider the function f(x) = x^2 - 6x + 8. Taking the derivative, we get f'(x) = 2x - 6. Setting this equal to zero and solving for x, we get x = 3. This means that the maximum or minimum point of the function occurs at x = 3. To determine whether it is a maximum or minimum, we take the second derivative: f''(x) = 2. Since the second derivative is positive, we know that the function has a minimum at x = 3.

In summary, the derivative of a function reveals the minimum or maximum value of the function without changing the form of the equation. By finding the zeros of the derivative and using the second derivative test, we can identify the location and type of the maximum or minimum point, equation that reveals the minimum or maximum value without changing its form. The quadratic equation, given by the general form y = ax^2 + bx + c, is an ideal example to consider.

A quadratic equation represents a parabola, which has either a minimum or maximum value depending on the coefficient "a". If "a" is positive, the parabola opens upwards and has a minimum value, and if "a" is negative, the parabola opens downwards and has a maximum value. The minimum or maximum value is located at the vertex of the parabola.

To find the x-coordinate of the vertex, you can use the formula x = -b/(2a). By plugging the values of "a" and "b" from the quadratic equation, you can determine the x-coordinate of the vertex. Then, you can substitute this x-coordinate back into the original equation to find the corresponding y-coordinate, revealing the minimum or maximum value of the function without changing its form.

To summarize, the quadratic equation y = ax^2 + bx + c is a suitable example that reveals the minimum or maximum value without altering the equation's form. By finding the vertex of the parabola using the formula x = -b/(2a), you can determine the minimum or maximum value of the function.

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The behavior of the function falls to the left and rises to the right.

Given function  f(x)=x^3-4x^2+7,

Firstly identify the degree of the function which is :

3

Now identify the leading coefficient which is :

1

Now, we know that if the degree is odd then the function ends in opposite direction.

And also the leading coefficient is positive which leads to rise of the graph to the right.

By using the degree and leading coefficient we can determine the behavior of the function by using  below statements ;

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

So the behavior of the function falls to the left and rises to the right.

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Answer:

Step-by-step explanation:

10.

11.

12.

13.

to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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Answer:

7 students play an instrument.

Calculation:

35=100%

20%=[20×35]÷100

=7

At least 88.9% of the data will reside within 6.4 and 8.0.

Chebyshev's theorem provides a range within which a certain percentage of data will reside, regardless of the shape of the distribution.

According to Chebyshev's theorem, at least (1 - 1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.

In this case, we want to determine the range within which at least 88.9% of the data will reside.

Since Chebyshev's theorem applies to any distribution, we can use it to find a minimum range for the given percentage.

Given that the mean of the quiz scores is 7.2 and the standard deviation is 0.4, we can calculate the range by considering the number of standard deviations required to capture at least 88.9% of the data.

Using Chebyshev's theorem, we can set up the following inequality:

1 - 1/k^2 = 1 - 1/[(0.889)^2] ≤ 1 - 1/1.29 ≤ 0.889.

Simplifying the inequality, we get:

1 - 1/1.29 ≤ 0.889,

0.2289 ≤ 0.889.

This implies that at least 88.9% of the data will fall within 0.2289 standard deviations from the mean.

To find the range, we multiply the standard deviation by 0.2289 and add/subtract this value from the mean:

Range = 7.2 ± (0.4 * 0.2289),

Range ≈ 7.2 ± 0.0916.

Therefore, the range within which at least 88.9% of the data will reside is approximately (6.4, 8.0).

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The probability of getting a total of 8 is 1/9 or 0.111. The probability of getting two up faces that are the same is 1/6 or 0.167. The combined probability is 0.278

This can be calculated by adding the individual probabilities together.  To get the probability of getting a total of 8, we need to look at the different combinations that add up to 8. There are nine possible combinations (1+7, 2+6, 3+5, 4+4, 5+3, 6+2, 7+1).

Therefore, the probability of getting a total of 8 is 1/9 or 0.111.  To get the probability of getting two up faces that are the same, we look at the different combinations of two dice. There are six possible combinations (1+1, 2+2, 3+3, 4+4, 5+5, 6+6).

Therefore, the probability of getting two up faces that are the same is 1/6 or 0.167.  The combined probability of getting a total of 8 or two up faces that are the same is 0.278. This can be calculated by adding the individual probabilities together (0.111 + 0.167 = 0.278).

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Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

Naomi's burger shack sold a total of 484 hamburgers today .Then  121 cheeseburgers were sold and 363 hamburgers were sold

Naomi's burger shack sold a total of 484 hamburgers today.

three times as many hamburgers were sold without cheese as were sold with cheeseburgers

how many cheeseburgers were sold?

according to the question

Hamburgers (H) + cheeseburgers (C) = 484

C + H =  484

H = 3C

we can solve these equation

C+ 3C = 484

4 C= 484

C = 121

then we can find H by putting the value of C

H = 3* 121 = 363

So, 121 cheeseburgers were sold and 363 hamburgers were sold

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Answer:

1000

Step-by-step explanation:

The area of the side walk is is 138.16m²

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.

The area of a circle is expressed as;

A = πr²

The area of the pathway = area of big circle - area of small circle

The diameter of the big circle = 20+4 = 24m

Area of big circle = 3.14 × 12²

= 452.16m²

Area of the small circle =

3.14 × 10²

= 314m²

therefore the of the path way = 452.16 - 314m²

= 138.16m²

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Answer:

-5x+12

Step-by-step explanation:

12 -5x

We can use the communitive property of addition to change the order.

The minus sign stays with the 5x

-5x+12

The integral ∫cf→ ⋅ dr→, where f→ = xi

To evaluate the integral ∫c(f→ ⋅ dr→), we need to calculate the dot product between the vector field f→ and the differential displacement vector dr→ along the curve defined by c. Let's proceed step by step.

Given:

f→ = xi→ + 4zyj→ + xk→

c is r→ = ti→ + t^2j→ + t^3k→, where 2 ≤ t ≤ 3.

First, we'll express the dot product f→ ⋅ dr→ in terms of t and then integrate with respect to t over the given interval.

f→ ⋅ dr→ = (xi→ + 4zyj→ + xk→) ⋅ (ti→ + t^2j→ + t^3k→)

= (xi→ ⋅ ti→) + (4zyj→ ⋅ t^2j→) + (xk→ ⋅ t^3k→)

= xt + 4z(t^2) + xt^3

= 2xt + 4zt^2 + t^3x

Now, we'll integrate the dot product over the interval [2, 3] with respect to t.

∫cf→ ⋅ dr→ = ∫2t to 3t (2xt + 4zt^2 + t^3x) dt

= ∫2t to 3t 2xt dt + ∫2t to 3t 4zt^2 dt + ∫2t to 3t t^3x dt

Integrating each term separately:

∫2t to 3t 2xt dt = x∫2t to 3t 2t dt

= x[t^2] evaluated from 2t to 3t

= x[(3t)^2 - (2t)^2]

= x(9t^2 - 4t^2)

= 5xt^2

∫2t to 3t 4zt^2 dt = 4z∫2t to 3t t^2 dt

= 4z[(1/3)t^3] evaluated from 2t to 3t

= 4z[(1/3)(3t)^3 - (1/3)(2t)^3]

= 4z[(1/3)(27t^3) - (1/3)(8t^3)]

= 4z(9t^3 - 8t^3)

= 4zt^3

∫2t to 3t t^3x dt = x∫2t to 3t t^3 dt

= x[(1/4)t^4] evaluated from 2t to 3t

= x[(1/4)(3t)^4 - (1/4)(2t)^4]

= x[(1/4)(81t^4) - (1/4)(16t^4)]

= x(65t^4)

Now, we can evaluate the integral:

∫cf→ ⋅ dr→ = 5xt^2 + 4zt^3 + 65t^4

Finally, to express the result in terms of c, we substitute c = r→:

∫cf→ ⋅ dr→ = 5c^2 + 4cz^2 + 65c^4

Therefore, the integral ∫cf→ ⋅ dr→, where f→ = xi

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