Part A: What is the shortest distance between the gymnasium and the library? Round your answer to the nearest tenth of a kilometer.


Part B: Gabe walks the shortest distance from his house to the gymnasium, then the shortest distance to the library. What is the total distance Gabe walked?

After performing the chi square test on the data given we get the result as false, therefore we will reject the null hypothesis.

In this instance, the goodness of fit will be assessed using a Chi-square test.

The hypothesis are ,

H0 : The frequencies that were seen match those that were anticipated.

H1  : The observed and predicted frequencies are not the same.

The following is the test statistic:

X² = ( O - E )² / E

The values in the table are computed.

75.10 is the test statistic value.

The test's degrees of freedom are:

n - 1 = 4 - 1 = 3

0.00001 = p-value

0.05 is the p-value, which is 0.00001 as per Chi square table.

So, at whatever level of significance, the null hypothesis will be disproved.

Therefore, there is enough data to disprove the idea that age-related crash rates are inversely correlated with driving rates.

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The creation of a scatter plot is the first step in the analysis of two quantitative variables.

A scatter plot is a form of a graph where each data point is shown separately to show the relationship between two quantitative variables. A scatter plot graph shows the link between the variables to one another after learning the concept of a sample statistic through examples.

In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.

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Answer:

$50

Step-by-step explanation:

To find the original price, divide the new price by the 0.7, since the discount was 30%:

35/0.7

= 50

So, the original price of the game was $50

Answer:

$50

Step-by-step explanation:

.3 multiplied by 50= 15, then add 15 to 35 to get 50

Answer:

a) To find the time it will take William to cover the path shown on the map, we need to convert the length of the path from centimeters to kilometers using the map scale. 1 cm on the map represents 40,000 cm in reality, which is equivalent to 0.4 km. So, the length of the path in kilometers is:

36 cm x 0.4 km/cm = 14.4 km

Now we can use the formula time = distance ÷ speed to find how long it will take William to cover the path:

time = distance ÷ speed = 14.4 km ÷ 5 km/h = 2.88 hours or 2 hours and 52.5 minutes (rounded to the nearest minute).

b) The area of the rectangular field can be found by multiplying its dimensions together, then converting the area from square centimeters to hectares using the scale of the map.

Area of field = 9 cm x 7 cm = 63 cm²

Area of field in hectares = 63 cm² ÷ (20,000 cm/ha)² = 0.0001575 ha

To find how many tons of barley the farmer needs, we can use the given conversion factor of 0.3 tons of barley per hectare:

Tons of barley needed = 0.0001575 ha x 0.3 tons/ha = 0.00004725 tons or 47.25 grams of barley.

c) To find the area of the pool in reality, we need to convert the area of the pool on the map from square centimeters to square meters using the map scale.

Area of pool on map = 18.84 cm²

Area of pool in reality = 18.84 cm² x (500 cm/m)² = 0.471 m²

d)

1) The length of the straight edge of the figure can be found using the Pythagorean theorem:

a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

c = √25 = 5 cm

The area of the figure can be found by adding the area of the triangle and the semicircle:

Area of triangle = 1/2 x base x height = 1/2 x 3 cm x 4 cm = 6 cm²

Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5/2)² = 19.63 cm²

Total area of figure = 6 cm² + 19.63 cm² = 25.63 cm²

2) To draw the figure on a scale of 1:2, we need to multiply all dimensions by 2. So, the straight edge of the figure would be 10 cm long, the base of the triangle would be 6 cm, and the height of the triangle would be 8 cm. The radius of the semicircle would be 5 cm.

Using the same calculations as before, we can find the area of the figure on the new scale:

Area of triangle = 1/2 x base x height = 1/2 x 6 cm x 8 cm = 24 cm²

Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5 cm)² = 39.27 cm²

Total area of figure = 24 cm² + 39.27 cm² = 63.27 cm²

3) To find the length and area of the figure twice its original size, we need to multiply all dimensions by 2. So, the straight edge of the figure would be 10 cm long, the base of the triangle would be 6 cm, and the height of the triangle would be 8 cm. The radius of the semicircle would be 5 cm.

Using the same calculations as before, we can find the area of the figure on the new scale:

Area of triangle = 1/2 x base x height = 1/2 x 6 cm x 8 cm = 24 cm²

Area of semicircle = 1/2 x π x radius² = 1/2 x π x (5 cm)² = 39.27 cm²

Total area of figure = 24 cm² + 39.27 cm² = 63.27 cm²

e) Without knowing the specific proportion, it's difficult to provide a solution. Please provide more information or the specific proportion so that we can help you solve it.

The total number of different choices for mother and child of the year is the product of both the mother and the child choices. So, there are 30 different choices possible.

There are 10 women in the community, and we can choose one of them in 10 different ways. For each chosen woman, we can then choose one of her three children in 3 different ways.

Therefore, the total number of different choices for mother and child of the year is the product of the number of choices for the mother and the number of choices for her child.

This can be written as follows:

10 (choices for the mother)* 3(choices for the child) = 30

So there are 30 different choices possible for mother and child of the year in this community.

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Answer:

1) Velocity

\(v(t) = -4\cdot t^{3}+36\cdot t^{2}\)

Acceleration

\(a(t) = -12\cdot t^{2}+72\cdot t\)

2) Velocity

\(v(t) = -4\cdot t^{3}+24\cdot t^{2}\)

Acceleration

\(a(t) = -12\cdot t^{2}+48\cdot t\)

Step-by-step explanation:

From Physics we remember that velocity (\(v(t)\)) and acceleration (\(a(t)\)) are the first and second derivatives of the function position in time. That is:

1) Let \(s(t) = -t^{4}+12\cdot t^{3}\), where \(t \ge 0\). The functions velocity and aceleration are, respectively:

Velocity

\(v(t) = -4\cdot t^{3}+36\cdot t^{2}\)

Acceleration

\(a(t) = -12\cdot t^{2}+72\cdot t\)

2) Let \(s(t) = -t^{4}+8\cdot t^{3}\), where \(t\ge 0\). The functions velocity and acceleration are, respectively:

Velocity

\(v(t) = -4\cdot t^{3}+24\cdot t^{2}\)

Acceleration

\(a(t) = -12\cdot t^{2}+48\cdot t\)

Answer:

\(\sf D) \quad s=8 \frac{1}{4}t\)

Step-by-step explanation:

Therefore, if the rate of cleaning is 8 1/4 square feet per hour, the relationship between s and t is:

\(\sf s=8 \frac{1}{4}t\)

Answer:

wyatt

Step-by-step explanation:

4:30 mins is 270 seconds

Answer:

\(\Huge \fbox{72 mph}\)

Step-by-step explanation:

Step 1:

Convert \(\bold{32 m/s}\) to \(\bold{km/h}\) by multiplying by 3.6 (since \(\bold{1 m/s}\) = \(\bold{3.6 km/h}\))

\(\large \text{32 m/s $\times$ 3.6 = 115.2 km/h}\)

Step 2:

Convert \(\bold{115.2 km/h}\) to \(\bold{mph}\) using the given conversion factor of \(\bold{8 km/h = 5 mph}\)

\(\large \text{115.2 km/h $\div$ 8 km/h = 14.4}\\\text{14.4 $\times$ 5 mph = 72 mph}\)

Therefore, \(\bold{32 m/s}\) is equivalent to \(\bold{72 mph}\).

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

In the standard conversion unit, 32 m/s equals 72 mph in mph

The conversion equation is given as

\(\sf 8 \ km/h = 5 \ mph\)

Convert 8 km to meters

So, we have the following equation

\(\sf 8 \times 1000 \ m/h = 5 \ mph\)

Evaluate the products

So, we have the following equation

\(\sf 8000 \ m/h = 5 \ mph\)

Convert 1 hour to seconds

So, we have the following equation

\(\sf 8000 \ m/3600 s = 5\ mph\)

Evaluate the quotient

So, we have the following equation

\(\sf \dfrac{20}{9} \ m/s = 5 \ mph\)

Multiply both sides by 9/20

\(\sf 1 \ m/s = \dfrac{9}{20} \times 5 \ mph\)

Multiply both sides by 32

\(\sf 32 \times 1 \ m/s = 32 \times \dfrac{9}{20} \times 5 \ mph\)

Evaluate the products

\(\sf 32 \ m/s = 72 \ mph\)

Hence, the equivalent of 32 m/s in mph is 72 mph

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Answer:

Hopeiit helped...

Please mark as brainliest...thanks!!!

Thanks!!!!!!!!!!!!

Step-by-step explanation:

Distance formula. Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.

The Distance Formula is a variant of the Pythagorean Theorem that you used back in geometry. Here's how we get from the one to the other:

Suppose you're given the two points (–2, 1) and (1, 5), and they want you to find out how far apart they are.

You can draw in the lines that form a right-angled triangle, using these points as two of the corners:

It's easy to find the lengths of the horizontal and vertical sides of the right triangle: just subtract the x-values and the y-values:

Then use the Pythagorean Theorem to find the length of the third side (which is the hypotenuse of the right triangle):

This format always holds true. Given two points, you can always plot them, draw the right triangle, and then find the length of the hypotenuse. The length of the hypotenuse is the distance between the two points. Since this format always works, it can be turned into a formula:

Distance Formula: Given the two points (x1, y1) and (x2, y2), the distance d between these points is given by the formula:  d=√((x_2-x_1)²+(y_2-y_1)²)

Credits:

Distance formula | Analytic geometry (video) | Khan Academy

Purple Math

Answer: -19.2

Step-by-step explanation:

Answer:

Ok so you have to figure out what is the input, output, y-intercept (b), slope (m), and equation.

First, input is the x. Looking at the graph.

Input : 0, 10, 20

Second, output is the y. Looking at the graph.

Output : 20, 30, 40

Third, y-intercept is the b in the equation of y = mx + b. Looking at the graph.

Y-intercept (b) : 20

Fourth, slope is the m in the equation of y = mx + b. Looking at the graph.

Slope (m) : 1/2

Fifth, you have to find the equation in the form of y = mx + b. Looking at the graph.

Equation : y = 1/2x + 20

I hope this helps and if you have any other questions I would be glad to answer it, thank you :) !!

Answer:

volume of cylinder is πr²h so whatever your radius is then square it multiply by height. don't multiply by pi as it gives it to you in the answer

The Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

Define Domain and Range

Given expression is,

f(x) = -1/4x³ + 4x - 3

In this x ∈ R, so

Domain = (-∞,∞) , { x|x  ∈ R }

Range =   (-∞,∞) ,{ y|y ∈ R }

Hence, the Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

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Answer: $8.50

Step-by-step explanation:

The expected gain (loss) is a weighted average of the probability of the different gains (losses) and the gains or losses.

Expected gain or loss for stock JKL:

= (Probability of losing $25 * -25) + ( Probability of gaining $5 * 5) + ( Probability of gaining $45 * 45)

= (15% * -25) + (65% * 5) + (20% * 45)

= -3.75 + 3.25 + 9

= $8.50

Answer:8.50$

Step-by-step explanation:

Answer:

BC = \(\frac{12}{13}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

BC² + AC² = AB²

BC² + (\(\frac{5}{13}\) )² = 1²

BC² + \(\frac{25}{169}\) = 1 ( subtract \(\frac{25}{169}\) from both sides )

BC² = \(\frac{169}{169}\) - \(\frac{25}{169}\) = \(\frac{144}{169}\) ( take square root of both sides )

BC = \(\sqrt{\frac{144}{169} }\) = \(\frac{12}{13}\)

1. 10 * 10 * 10 = 1000 = 10^3

2. 10 * 10 * 10 * 10 = 10,000 = 10^4

3. 10 * 10 * 10 * 10 * 10 = 100,000 = 10^5

4. 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10,000,000 = 10^7

5. Summary

Multiplication   Exp on first factor   Exp on 2nd factor    Exp on product

10^1 * 10^2                 1                                    2                             3

10^1 * 10^3                 1                                    3                              4

10^2 * 10^3               2                                   3                              5

10^4 * 10^3               4                                   3                              7

6. Multiplying two powers of ten, the product can be found by adding up the exponential values, the sum will be the exponent of the product and the base remain ten.

This refers to the exponential value of 10. Hence we can say that power as used in mathematics, is also called exponents.

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2x+10=28

2x=18

x=9

Please give me brainliest!

Answer: A

Step-by-step explanation:

A random variable X has a probability distribution as follows:

X = 0, 1, 2, 3

P(X) = 2k, 3k, 13k, 2k

where k is a positive constant. The probability P(X < 2.0) is 0.25.

What is random variable?

A quantity or item that depends on random events is formalised mathematically as a random variable, also known as a random quantity, aleatory variable, or stochastic variable. It is a function or mapping from potential outcomes to a quantifiable space, frequently to real numbers.

We know that probability sum of all events is 1

Therefore here sum of all probability events =P(X=0)+P(X=1)+P(X=2)+PX=3)=1

2k+3k+13k+2k=1

20k=1

k=1/20=0.05

For P(x<2)=P(X=0)+P(X=1)=2k+3k =5k=5*(1/20)=0.25

Hence the correct answer is b, 0.25

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Answer:

10

Step-by-step explanation:

Answer:

\(40... = = > > < .01\)

Answer

-19.2

Step-by-step explanation:

Answer:

-19.2

Step-by-step explanation:

Yes

The probability that a child was living with just one parent is 0.322

The probability that a randomly selected child in a country was living with his or her mother as the sole parent was 0.242

P(mother as sole parent) = 0.242

The probability that a randomly selected child in a country was living with his or her father as the sole parent was 0.080

P(father as sole parent) = 0.080

P(A U B) = P(A) + P(B) - P(A∩ B)

P(living with just one parent) = P(mother as sole parent) + P(father as sole parent)

P(living with just one parent)  = 0.242 + 0.080 = 0.322

Therefore, the probability that a child was living with just one parent is 0.322

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Answer:

Hello,

a=0.5

Step-by-step explanation:

\(\left \{ \begin{array}{ccc}ax+2y&=&12\\8x+32y&=&144\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}ax+2y&=&12\\x+4y&=&18\\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}(1-2a)x&=&-6\\x+4y&=&18\\\end{array}\right.\\\\if\ 1-2a\neq 0\ (or\ a\neq \dfrac{1}{2} )\ then\\\left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{18-\dfrac{6}{2a-1}}{4} \\\end{array}\right.\\\\\)

\(\Longleftrightarrow\ \left \{ \begin{array}{ccc}x&=&\dfrac{6}{2a-1}\\\\y&=&\dfrac{ 3(3a-2)}{2a-1} \\\end{array}\right.\\\\\)

else\

\(a=\dfrac{1}{2} \\\Longleftrightarrow\ \left \{ \begin{array}{ccc}\dfrac{1}{2} x+2y&=&12\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}x+4y&=&24\\\\x+4y&=&18 \\\end{array}\right.\\\\\\\Longleftrightarrow\ \left \{ \begin{array}{ccc}0=6\ !!!!!\\\end{array}\right.\\\\Syetem\ has\ no\ solution\\\)

Answer:

5.5

Step-by-step explanation:

180/3 =60 (60/1 hr)

330/60 =5.5

Answer: 3x-3 apex

Step-by-step explanation: