A map has a scale of 1 inch : 40 miles. Use the given map distance to find the actual distance.

1.) 12 inches
2.) 1 foot

Answer:

Willis Towers is 1.7 times bigger than the Transamerica pyramid

Step-by-step explanation:

The Willis Tower In Chicago is 1,451 FEET tall. The Transamerica Pyramid is San Francisco is 10,236 INCHES tall. How do these two compare?

Note that

1 foot = 12 inches

We convert the height of willis tower to inches

1 foot = 12 inches.

1,451 feet = x inches

Cross Multiply

x = 1451 × 12 inches

x = 17412 inches

Comparing the two buildings

Willis Tower : Transamerica pyramid

1,7412 inches : 10,236 Inches

= 1.7010550996 : 1

Therefore,

Willis Towers is 1.7 times bigger than the Transamerica pyramid

328 hope this helps

The value of the integral ∫(3z + 1) / (z^2 + 2) dz, where C is the constant is ln|z^2 + 2| + 3/√2 arctan(z/√2) + C.

To evaluate the given integral, we first need to break it down using partial fraction decomposition. Therefore, we have:

(3z + 1) / (z^2 + 2) = (Az + B) / (z^2 + 2)

Multiplying both sides by (z^2 + 2), we get:

3z + 1 = (Az + B)

We now need to find the values of A and B. Setting z = 0, we get:

1 = B

Setting z = 1, we get:

3 + 1 = A + B
A = 2

Therefore, the integral becomes:

∫ (2z + 1) / (z^2 + 2) dz

We can now integrate using substitution, with u = z^2 + 2 and du/dz = 2z. This gives us:

∫ (2z + 1) / (z^2 + 2) dz = ∫ (1/u) du
= ln|u| + C
= ln|z^2 + 2| + C

Using trigonometric substitution, we can also evaluate the integral in terms of arctan:

Let z = √2 tanθ, dz = √2 sec^2θ dθ. Then the integral becomes:

∫ (3z + 1) / (z^2 + 2) dz = ∫ (3√2 tanθ + 1) / (2tan^2θ + 3) √2 sec^2θ dθ
= 3/√2 ∫ (tanθ) / (tan^2θ + (3/2)) d(tanθ) + 1/√2 ∫ (1) / (tan^2θ + (3/2)) dθ
= 3/√2 ln|tan^2θ + (3/2)| + 3/√2 arctan(tanθ/√2) + C
= 3/√2 ln|z^2 + 2| + 3/√2 arctan(z/√2) + C

Thus, we get the same result as before.

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Answer:

7 minutes

Step-by-step explanation:

From the question :

Descent = ascent

Initial height * descent rate = initial position * ascent rate

Plane on ground is at an initial position or height of 0

42000 - 3300t = 0 + 2700t

Where, t = time

-3300t - 2700t = 0 - 42000

-6000t = - 42000

t = 42000 / 6000

t = 7 minutes

Answer:

12 months at 6.25%

Step-by-step explanation:

You deposit $1250 into a bank account paying 6.25% simple interest per month. You left the money in for 12 months. Find the interest earned and the amount at the end of those 12 months?

Result:

The interest is $937.5 and the amount is $2187.5.

Explanation:

STEP 1: Convert interest rate of 6.25% per month into rate per year.

STEP 2: Convert 12 months into years.

STEP 3: Find an interest by using the formula , where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this examplee P = $1250, i = 75% and t = 1 years, so

STEP 4: Find an amount by using the formula .

Since P = $1250 and I = $937.5 we have

Answer:

The option that describe the effect of the change is;

Step-by-step explanation:

The parameters from the question are;

The (scale) factor by which the base and the height of the triangle are multiplied = 5/4

By the constant proportion of their sides, the triangle before and the triangle obtained after the multiplication are similar

Let 'a' and 'b' represent the length of the base and the height of the triangle respectively, we have;

The area of the triangle, A₁ = 1/2 × a × b = a·b/2

With the application of the scale factor of 5/4, we have;

The area of the scaled triangle, A₂ = 1/2 × (5/4) × a × (5/4) × b = (5/4)² × a·b/2

Therefore, the scale factor of the area = (5/4)²

The scale factor of the perimeter = √(The scale facto of area)

∴ The scale factor of the perimeter = √(5/4)² = (5/4)

The scale factor of the perimeter = (5/4)

Therefore, the perimeter of the scaled triangle is obtained by multiplying the perimeter of the initial triangle by (5/4).

Answer:

The perimeter is multiplied by 5/4.

Step-by-step explanation:

Answer:

y = - 3 x - 5

Step-by-step explanation:

find the negative reciprocal of the slope of the original line use the point slope formula y - y 1 = m ( x - x 1 ) to find the line perpendicular to 3 y = x + 6

hope this helps

The most accurate estimate of the population mean is 32 pounds, based on the sample data.

The best point estimate of the mean can be obtained by using the sample mean as an estimate for the population mean.

Given that the sample mean of the number of pounds that the 60 overweight men were overweight is 32, the best point estimate of the mean is also 32 pounds.

Therefore, the best point estimate of the mean is 32 pounds.

Mean: The term "mean" refers to a measure of central tendency. It is often referred to as the average of a set of numbers. The mean is calculated by adding up all the values in the set and dividing the sum by the total number of values.

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Based on the normal probability plot constructed for the octane data, it does not appear reasonable to assume that the octane rating is normally distributed. The plot deviates significantly from a straight line, indicating a departure from normality.

A normal probability plot is a graphical tool used to assess whether a dataset follows a normal distribution. In a normal plot, the observed data points are plotted against the corresponding quantiles of a theoretical normal distribution. If the data points fall approximately along a straight line, it suggests that the data can be reasonably modeled as normally distributed.

In this case, when constructing the normal probability plot for the octane data, if the plot deviates significantly from a straight line, it indicates a departure from normality. If the points on the plot show a distinct curvature or exhibit systematic patterns, it suggests that the data does not follow a normal distribution.

By examining the sketch of the normal probability plot for the octane data, if it shows substantial deviations from a straight line, with points deviating from the expected pattern, it implies that the octane rating is not normally distributed. This departure from normality could be due to various factors, such as skewness, outliers, or a different underlying distribution that better fits the data. Therefore, based on the sketch of the plot, it is reasonable to conclude that the octane rating is not normally distributed.

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Answer:

(a) 6688 divided by 88 = 76

(b) 312 - 73 = 239

Answer:

130⁰. unsure. angle sum, 25+25+x =180, so x=180-25-25

If x - y = 3

Work out the value of 5(x - y)

x - y = 3 ( Given )

[tex] \therefore [/tex] 5(x - y) = 5 × 3 = 15 [ as x - y = 3 ]

_____________________________________

If x - y = 3

Work out the value of 2x - 2y

x - y = 3 ( Given )

[tex] \therefore [/tex] 2x - 2y = 2(x - y) = 2 × 3 = 6 [ as x - y = 3 ]

_____________________________________

If x - y = 3

Work out the value of y - x

x - y = 3 ( Given )

[tex] \therefore [/tex] y - x = -3 [ as x - y = 3 ]

_____________________________________

Answer:

1

Step-by-step explanation:

The area between the curve y = x² + 3x - 28 and the x-axis, from x = -8 to x=0 is 64/3 square units.

We want to calculate the integral of the absolute value of the function over the given interval:

Area = ∫[from -8 to 0] |x² + 3x - 28| dx

Since the curve lies below the x-axis between x = -7 and x = 4, we need to split the integral into two parts and change the sign of the function for the interval [-7, 4]

Area = ∫[from -8 to -7] -(x² + 3x - 28) dx + ∫[from -7 to 4] (x² + 3x - 28) dx + ∫[from 4 to 0] -(x² + 3x - 28) dx

We can now integrate each part separately:

Area = -∫[from -8 to -7] (x² + 3x - 28) dx + ∫[from -7 to 4] (x² + 3x - 28) dx - ∫[from 4 to 0] (x² + 3x - 28) dx

Simplifying, we get:

Area = [-1/3 x³ - 3/2 x² + 28x] [from -8 to -7] + [1/3 x³ + 3/2 x² - 28x] [from -7 to 4] - [-1/3 x³ - 3/2 x² + 28x] [from 4 to 0]

Area = [(-1/3(-7)³ - 3/2(-7)² + 28(-7)) - (-1/3(-8)³ - 3/2(-8)² + 28(-8))] + [(1/3(4)³ + 3/2(4)² - 28(4)) - (1/3(-7)³ - 3/2(-7)² + 28(-7))] - [(-1/3(0)³ - 3/2(0)² + 28(0)) - (-1/3(4)³ - 3/2(4)² + 28(4))]

Area = [(343/3 + 147 - 196) - (-512/3 + 96 - 224)] + [(64/3 + 24 - 112) - (-343/3 + 147 - 196)] - [0 - (-64/3 + 24 - 112)]

Area = [(343/3 + 147 - 196) - (-512/3 + 96 - 224)] + [(64/3 + 24 - 112) - (-343/3 + 147 - 196)] - (-64/3 + 24 - 112)

Area = (64/3)

Therefore, the area between the curve y = x² + 3x - 28 and the x-axis from x = -8 to x = 0 is 64/3 square units.

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Answer:

2/35

Step-by-step explanation:

[tex]\frac{3}{7}[/tex] × [tex]\frac{2}{15}[/tex]

[tex]\frac{1}{7}[/tex] x [tex]\frac{2}{5}[/tex]

= 2/35

Answer:

its c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

great job mate

Answer:

Solution : Let Tn=0. Then,21+(n-1)×(-3)=0⇒n=8. So, 8th term is zero.

Step-by-step explanation:

Answer:

Kristy makes 16 per hour.

Step-by-step explanation: Divded 48 by 3.

The formula for calculating confidence interval is: $\overline{X} \pm Z_{\alpha/2}\frac{σ}{\sqrt{n}}$,

where $\overline{X}$ is the sample mean,

$σ$ is the population standard deviation,

$n$ is the sample size, and $Z_{\alpha/2}$ is the critical value of the standard normal distribution at $\alpha/2$ and $(1-\alpha/2)$ levels of significance respectively. To construct the 90% confidence interval for the given data: n = 240p-hat = 0.55The sample mean is equal to p-hat which is 0.55. Therefore, the margin of error is given by;

ME = Z_{α/2} × √{p-hat(1 - p-hat) / n}α = 0.10, thus α/2 = 0.05, so the area to the right of the critical value is equal to 0.05.

Using the standard normal distribution table, the critical value for α/2 = 0.05 is: Z_{α/2} = 1.64

Therefore, the confidence interval is given by; CI = p-hat ± Z_{α/2} × √{p-hat(1 - p-hat) / n}CI = 0.55 ± 1.64 × √{0.55(1 - 0.55) / 240}CI = 0.55 ± 0.077

Therefore, the confidence interval is (0.473, 0.627) (rounded to three decimal places).

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a)  the venture capitalist has three investment options: a social media company, an advertising firm, and a chemical company.

b) The advertising firm has the highest expected return, making it the most profitable choice.

c) The investment with the highest expected return is Investment 2 (the advertising firm) with an expected value of $1,200,000.

d) The safest investment is Investment 3 (the chemical company) because it has the highest probability (50%) of not incurring any loss (no profit, but no loss either).

e) The riskiest investment is Investment 1 (the social media company) because it has a 50% chance of losing the entire $1,000,000 investment, which is the highest probability of loss among the three investments.

a. Probability Distribution for each investment:

Investment 1 (Social Media Company):

X (Profit/Loss) P(X)

$7,000,000 0.20

$0 0.30

-$1,000,000 0.50

Investment 2 (Advertising Firm):

X (Profit/Loss) P(X)

$3,000,000 0.10

$2,000,000 0.60

-$1,000,000 0.30

Investment 3 (Chemical Company):

X (Profit/Loss) P(X)

$3,000,000 0.40

$0 0.50

-$1,000,000 0.10

b. Expected value for each investment:

Expected value (Investment 1):

E(X) = ($7,000,000 × 0.20) + ($0 × 0.30) + (-$1,000,000 × 0.50)

= $1,400,000 + $0 - $500,000

= $900,000

Expected value (Investment 2):

E(X) = ($3,000,000 × 0.10) + ($2,000,000 × 0.60) + (-$1,000,000 × 0.30)

= $300,000 + $1,200,000 - $300,000

= $1,200,000

Expected value (Investment 3):

E(X) = ($3,000,000 × 0.40) + ($0 × 0.50) + (-$1,000,000 × 0.10)

= $1,200,000 + $0 - $100,000

= $1,100,000

c. Investment with the highest expected return:

The investment with the highest expected return is Investment 2 (the advertising firm) with an expected value of $1,200,000.

d. Safest investment:

The safest investment is Investment 3 (the chemical company) because it has the highest probability (50%) of not incurring any loss (no profit, but no loss either).

e. Riskiest investment:

The riskiest investment is Investment 1 (the social media company) because it has a 50% chance of losing the entire $1,000,000 investment, which is the highest probability of loss among the three investments.

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Answer:

21

Step-by-step explanation:

7 * 3 =21

[tex]\log_7x=\dfrac{1}{2}\\\\x=7^{1/2}\\\\x=\sqrt{7}\approx2.646[/tex]

Answer:

1.

Step-by-step explanation:

1. 4 + 2 = 6

2. 4 - 4 = 0

3. 10 + 4 = 14

4. 4 - 10 = -6

number 1 is the right answer

Answer:

1.

Step-by-step explanation:

Answer:

6

Step by step explanation:

8 × ¾ = ²⁴⁄₄ = 6

Answer:

6

Step-by-step explanation:

You can solve this equation in multiple ways:

1) Change [tex]\frac{3}{4}[/tex] into a decimal

2) Change [tex]8[/tex] into a fraction, and multiply that way.

The p-value for testing the hypothesis that the average runtime of HP laptops is not equal to 120 minutes, based on a sample mean of 125 minutes from a sample of 50 laptops, cannot be determined without additional information.

To calculate the p-value, we need the population standard deviation or the t-value associated with the sample mean and the degrees of freedom. The p-value represents the probability of observing a sample mean as extreme or more extreme than the observed sample mean, assuming the null hypothesis is true.

However, since the population standard deviation is not provided in the question, we cannot directly calculate the p-value. Similarly, the degrees of freedom for the t-distribution depend on the sample size and are not given.

To determine the p-value, we would need either the population standard deviation or the t-value associated with the sample mean and the degrees of freedom. With this information, we could look up the p-value from the t-distribution table or use statistical software to obtain the p-value.

Therefore, without the necessary information, the p-value for the hypothesis test cannot be determined.

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Answer:

P = Parker

According to the question,

Equation for Jessica's height = 8 - 2P

The probability that a randomly selected card does not have a face value of 9 is approximately 0.9231 or 92.31%.

In a standard deck of 52 cards, there are 4 cards of each face value (Ace through 10) for each of the four suits (hearts, diamonds, clubs, and spades). Since the face value of 9 is one of the possible values, there are 4 cards with a face value of 9.

To find the probability that a randomly selected card does not have a face value of 9, we need to determine the number of cards that do not have this particular value. There are 52 cards in total, and we subtract the 4 cards with a face value of 9:

52 - 4 = 48

So, there are 48 cards that do not have a face value of 9. Therefore, the probability of selecting a card without a face value of 9 is:

P(not 9) = number of favorable outcomes / total number of outcomes
= 48 / 52
= 12 / 13
≈ 0.9231

The probability that a randomly selected card does not have a face value of 9 is approximately 0.9231 or 92.31%.

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Answer:

Relative frequency

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

it just is