Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip to Country A and Country B. Country A's currency is trading at $1.30 per currency A, and Country B's currency is trading at $1.60 per currency B. She plans to spend more time in Country A, so she wants to have four times as much of currency A as currency B. Set up and solve a system of equations to model this problem, and explain what the answer means in practical terms.

Using the t-distribution, it is found that since the p-value of the test is 0.0428 < 0.05, the sample provides convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price.

At the null hypothesis, it is tested if the mean is the same, that is:

\(H_0: \mu = 3.57\)

At the alternative hypothesis, it is tested if it is greater, that is:

\(H_1: \mu > 3.57\)

We can find the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

For this problem, two of the values of the parameters are: \(n = 8, \mu = 3.57\)

Additionally, with the help of a calculator: \(\overline{x} = 4.5225, s = 1.3468\)

The value of the test statistic is:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{4.5225 - 3.57}{\frac{1.3468}{\sqrt{8}}}\)

\(t = 2\)

The p-value of the test is found using a right-tailed test, as we are testing if the mean is greater than a value, with t = 2 and 8 - 1 = 7 df.

Since the p-value of the test is 0.0428 < 0.05, the sample provides convincing evidence that the mean May 2009 price of a Big Mac in Europe is greater than the reported U.S. price.

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Answer:

1498

Step-by-step explanation:

Answer:

The carts velocity= 2m/s

Step-by-step explanation:

It took Manuel 87 seconds to push a shopping cart directly to his car.

One third of 87 = 87/3 = 29

In 29 seconds the carts moved 58 meter's.

The carts velocity = distance/time

The carts velocity = 58/29

The carts velocity= 2m/s

Answer:

y=4x+2

Step-by-step explanation:

So we start with the slope, which is bad.

But I have an idea

lets write it as

y=4x+? and since x=1 and y=6

6=4+?

Therefore, the y, intercept must be two

Answer:

y=4x+2

Step-by-step explanation:

y-y1=m(x-x1)

y-6=4(x-1)

y=4x-4+6

y=4x+2

Answer:

The Answer is: 0.744747

Step-by-step explanation:

cos 45 + sin 160

0.525322 + 0.219425

0.744747

hope this helps if it wasn't too late lol

Answer:

-0.993

Step-by-step explanation:

ADD 3 and DIVIDE by -2 to get the natural log expression by itself on the left.

Then convert to an exponential equation. Ln means that the base is e (e is a special number,but in fact, just a number)

e^(-5) -1 can be calculated on a calculator. There is usually an e^x button, then enter -5 exponent. Lastly subtract one.

x = -0.993

See image

The compound interest is larger than the simple interest by $3071.31

Where, simple interest is $3060 and compound interest is $6131.31

Compound interest refers to the method of calculating interest on a principal amount and any accumulated interest that has already been earned. In other words, it is the process of earning interest on interest.

The amount of interest earned using both simple and compound interest over a period of 30 years.

Simple interest formula:

\(SI = P*r*t\)

Using this formula, here, r = \(4\frac{1}{4}\) % = 0.0425

We can calculate the simple interest earned over 30 years,

SI = 2400 * 0.0425 * 30 = $3060

Compound interest formula:

\(A = P(1 + \frac{r}{n} )^{nt}\)

Using this formula, we can calculate the amount of money in the account after 30 years:

\(A=2400(1 + \frac{0.0425}{4} )^{4*30}\) = $8531.31

So, the Compound Interest earned = $8531.31 - $2400 = $6131.31

Therefore, the compound interest is larger than the simple interest by:

$6131.31 - $3060 = $3071.31

This is because compound interest earns interest on the interest that is already earned, resulting in a higher total interest earned over time compared to simple interest, which only earns interest on the initial principal amount.

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According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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Remember that

An isosceles triangle has two equal sides and two equal angles

so

in this problem

we have an isosceles triangle

that means

Division

Multiplication

-14

Step-by-step explanation:

Answer:

Division

Multiplication

-14

Step-by-step explanation:

other person was corrrect

Answer:

1. h,k

2. -3, -5

3. 1, 7

4. 9, -2

5. -4, -6

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have to simplify this equation.

Like this:

The closest number to x is 19:

Solve:

x = 19.

Answer:

$0.90 per pen

2.70/3=.90

Answer:

Answer:

the number of grams in cherry ice cream and mint chocolate is 23 grams fat and 25 grams fat respectively

Step-by-step explanation:

Let us assume the number of grams in cherry ice- cream be x

And, the number of grams in mint chocolate be y

Now as per the question

The following equations should be used

2x + y = 71  ................... (1)

x  + 2y = 73.................(2)

Multiply 2 in equation 1

So,

4x + 2y = 142

x + 2y = 73

3x = 69

x = 23 grams fat

And, y is

2(23) + y = 71

y = 25 grams fat

hence, the number of grams in cherry ice cream and mint chocolate is 23 grams fat and 25 grams fat respectively

Answer:

each piece is = 3 m long

Step-by-step explanation:

20 /10= 2

a) The distance of the stone above ground level at any time t is given by h(t) = 950 + 4.9t², where h(t) is measured in meters and t is measured in seconds.

b) It takes approximately 13.93 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of approximately 136.04 m/s.

d) It takes approximately 16.75 seconds for the stone thrown downward with a speed of 6 m/s to reach the ground.

When objects are dropped or thrown from a height, their speed and position can be determined using physics equations. In this problem, we will calculate the distance, time, and velocity of a stone dropped from a tower.

First, we need to determine the equation for the height of the stone above the ground at any given time t. We can use the formula:

h(t) = h0 + vt + 0.5at²

where h0 is the initial height, v is the initial velocity (which is zero for a dropped object), a is the acceleration due to gravity (g = 9.8 m/s^2), and t is the time since the stone was dropped.

Using the given values, we can plug in the numbers and simplify:

h(t) = 950 + 0t + 0.5(9.8)t²

h(t) = 950 + 4.9t²

To find the time it takes for the stone to reach the ground, we need to set h(t) = 0 and solve for t:

0 = 950 + 4.9t^2

t^2 = 193.88

t ≈ 13.93 seconds

To find the velocity at which the stone strikes the ground, we can use the formula:

v = v₀ + at

where v₀ is the initial velocity (which is zero for a dropped object) and a is the acceleration due to gravity (g = 9.8 m/s²). We can plug in the values for t and solve for v:

v = 0 + 9.8(13.93)

v ≈ 136.04 m/s

Finally, if the stone is thrown downward with a speed of 6 m/s, we can use the same formula for h(t) as before, but with an initial velocity of -6 m/s. We can then find the time it takes to reach the ground using the same method as before:

h(t) = 950 - 6t + 0.5(9.8)t²

0 = 950 - 6t + 4.9t²

t² - 1.22t - 193.88 = 0

t ≈ 16.75 seconds

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Answer:

a) This is a continuous random variable because the set of possible values is an interval.

b) Height = 0.5

Graph attached.

c) P(Y≤1) = 0.5

Step-by-step explanation:

a) If the density curve of the outcomes has a constant height, we have a uniform distribution for values between 0 and 2 (outside this range, the density function has a value of 0).

This function is continous and has a value for each real number. The set of possible values has a is an interval between 0 and 2, all with equal probability (the ones that are otuside this interval have 0 probability, so they are not possible values).

b) The height is calculated so that the total area under the density curve has to be equal to 1.

Then, we have to calculate the integral between 0 and 2 of the density function:

\(\int\limits^2_0 {U(x)} \, dx =\int\limits^2_0 {H} \, dx =H\int\limits^2_0 dx=H(x_2-x_1)=H(2-0)=1\\\\2H=1\\\\H=0.5\)

The height is H=0.5

(Graph attached)

c) The probability can be calculated by integrating the density function (which is equal to the area under the curve) between 0 and 1, or using the graph.

With the graph, we see that the area is equal to the height (0.5) by the width of the interval (1), so the total area is 0.5 x 1 = 0.5.

The probability P(Y≤1) is equal to 0.5.

Using the uniform distribution, it is found that:

a)

This is a continuous random variable because the set of possible values is an interval.

b)

The height is \(\frac{1}{2}\), and the sketch is given at the end of this answer.

c)

P(Y ≤ 1) = 0.5

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

\(P(X < x) = \frac{x - a}{b - a}\)

In this problem, uniformly distributed between 0 and 2, thus \(a = 0, b = 2\).

Item a:

Values in an interval, thus continuous. Discrete are for sample spaces, which is not the case here.

Item b:

The height is:

\(h = \frac{1}{b - a} = \frac{1}{2}\)

The graph is sketched at the end of this answer.

Item c:

\(P(Y \leq 1) = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5\)

Thus, P(Y ≤ 1) = 0.5.

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The probability result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners.

The podcast host is polling the next 100 listeners who send her fan emails in order to find out how they like the show. The results of the poll show that 80 out of 90 listeners polled said they liked it. This result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners. This means that the results of the poll may not be reflective of the opinion of all of the podcast host's listeners. Furthermore, the results may be influenced by the volunteer bias, as the respondents may have volunteered to take part in the poll because they already liked the show and wanted to show their support. Additionally, the results may be affected by non-response bias, as those who chose not to take part in the poll may have different opinions than those who did.

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Answer:

Step-by-step explanation:

A stem-and-leaf plot is a kind of histogram in which the most significant digit of a data value is taken to be the "stem", and the "leaves" are a list of the least-significant digits of the data values. It is convenient to list the leaves in increasing order, to facilitate determining the quartiles in the data.

__

The 14 data set values can be represented by the plot below. Here, we have elected to use parentheses ( ) to identify the 1st and 3rd quartile values, and a slash / to signify the location of the median.

__

stem | leaves

3 | 7 8

4 | 3 (3) 7 9

5 | 0 / 0 3 4 (6) 9 9

6 | 0

_____

The first and third quartiles are 43 and 56, respectively. The median is 50.

Answer:

the answer is =118000

Step-by-step explanation:

$107,000+5,000+6,000=118000                                                                                   Its simple

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

Option A, 4

Step-by-step explanation:

f(-2) = -(-2)³-3×(-2)²+8

= 8-12+8

= 16-12

= 4

Part A: The probability of rolling a 5 is 1/6 or approximately 0.167. Part B: the probability of rolling an even number is 3/6 or 1/2 or 0.5.

Probability is a branch of mathematics concerned with measuring the likelihood or chance of an event occurring. It is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability is expressed as a number between 0 and 1, where 0 means that the event will not occur and 1 means that the event will definitely occur. For example, if the probability of an event is 0.5, it means that the event has an equal chance of occurring or not occurring. Probability is used in various fields, such as science, engineering, finance, and statistics, to make predictions and make decisions based on uncertain events.

Part A:

The number cube has six faces, and each face has an equal chance of landing face-up. Therefore, the probability of rolling a 5 is 1/6 or approximately 0.167.

Part B:

The even numbers on a number cube are 2, 4, and 6. There are three even numbers out of a total of six possible outcomes. Therefore, the probability of rolling an even number is 3/6 or 1/2 or 0.5.

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Answer: A . Not all 2 × 2 matrices have an inverse matrix. If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses.

Step-by-step explanation:

Note that the angle labeled ∠PQR is given as 70°

First, note that the Lengths of tangents drawn from external points to a circle are equal in length. This means that:

Length of PT = Lenght of TR

This makes Δ TPR and Isosceles Triangle.

This also makes ∠P = ∠R..............................1

Thus:

∠P + ∠R + ∠T = 180°

Given expression 1 above,

we can say:

x + x + 38° = 180°

Thatis 2x = 180 - 40

2x = 140°

x = 140/2

x = 70°

Note that Line TP is parallel to Line QR and Line PQ is a transversal line. Thus, ∠P and ∠Q are co-interior angles. This means that:

∠P + ∠Q = 180°

Recall that:

70 + 40 + ∠Q = 180°
∠Q = 180 -70 -40

∠Q = 70°

Thus: ∠ PQR = 70°

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Full Question:

See attached image.

The probability of getting-

Probability is the measure of how likely an event is to occur. Many events are impossible to predict to absolute certainty. We can only predict the possibility of an event occurring, i.e. how likely it is to occur, using it.

The formula for probability is;

Probability(event) = favourable outcome/ total outcome

Now, as per the given question;

There are 27 papers put in a hat numbering from 1 to 27.

The sample space will  be;

s = {1,,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27}

The total outcome is 27.

The total number of 12 digit in the sample space is 1.

Thus, the probability for getting slip 12 is;

Probability(slip 12) = 1/27

The sample space for even number are;

s = {2,4,6,8,10,12,14,16,18,20,22,24,26}

Now, there are total number of even digits in the sample space is 13.

Thus, the probability for getting even number is;

Probability(even) = 13/27.

The sample space for prime number are;

s = {2,3,5,7,11,13,17,19,23}

Noe, the total number of prime digits in the sample space is 9.

Thus, the probability for getting prime number is;

Probability(prime) = 9/27 = 1/3

Therefore, the probability for getting the prime number is 1/3.

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The least amount of water was lost at Lake Stockton. It's best to choose C.

Given that,

Three lakes lost water. Lake Stockton lost 246, 3 hundredths of its water, Lake Parlor lost 85% of its water, and Lake Jensen lost \(\frac{5}{6}\) of its water.

Percentage is calculated by multiplying the ratio of a material's composition to the total composition of a material by 100.

Here, the percentage of each lake following the draught is equal, i.e.

Lake Jensen = \(\frac{5}{6}\) =83.33%

Lake Parlor =85%

Lake Stockton =\(\frac{246}{300}\)=82%

Therefore, from obtaining a fraction we got the least amount of water was lost at Lake Stockton. It's best to choose C.

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Answer: Lake Stockton

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