You have $50 in your wallet at the mall and buy a new pair of jeans and now you only have $16 in your wallet how much did the jeans cost

The approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41

The given parameters are:

Mean, μ = 89.46

Standard deviation, σ = 2.31

The z-score at x = 90 is calculated using

\(z = \frac{x - \mu}{\sigma}\)

This gives

\(z = \frac{90 - 89.46}{2.31}\\\)

Evaluate

z = 0.234

The probability is then calculated as:

P(x >90) = P(z > 0.234)

From z table of probabilities, we have:

P(x >90) = 0.41

Hence, the approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41

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The first option is correct.

You could do all the math to compare the final answers, but I looked at the part where you add. Using a standard algorithm, when going on to the next digit in the second number, you always add a 0 first. The rest of those options don't include a 0.

To show that two sides of one triangle are proportional to two corresponding sides of another triangle, with the included corresponding angles being congruent, you can use the Side-Side-Side (SSS) similarity criterion.

The SSS similarity criterion states that if the corresponding sides of two triangles are proportional and their corresponding angles are congruent, then the triangles are similar.
To prove this, follow these steps:

1. Given two triangles, let's call them triangle ABC and triangle DEF.
2. Identify two corresponding sides in each triangle that you want to show are proportional. Let's say AB and DE.
3. Also, identify the corresponding included angles, which are the angles formed by the corresponding sides. Let's say angle BAC and angle EDF.
4. Using the given information, state that AB/DE = BC/EF.
5. Now, prove that angle BAC = angle EDF. You can do this by showing that the two angles have the same measure or that they are congruent.
6. Once you have established that AB/DE = BC/EF and angle BAC = angle EDF, you can conclude that triangle ABC is similar to triangle DEF using the SSS similarity criterion.
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Answer:

A scale factor is a number which scales, or multiplies, some quantity.

Answer:

The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

Step-by-step explanation:

The ladder slipped approximately 289 cm down the wall.

To determine how far down the wall the ladder slipped, we can consider the ladder as the hypotenuse of a right triangle formed with the wall.

Initially, the ladder forms a right triangle with the wall and the ground, where the base (foot of the ladder) is 80 cm away from the wall. Let's denote the distance the ladder slipped down the wall as d cm.

Using the Pythagorean theorem, we have:

(80 cm)^2 + d^2 = (300 cm)^2

Simplifying the equation, we get:

6400 cm^2 + d^2 = 90000 cm^2

Rearranging the equation and solving for d, we have:

d^2 = 90000 cm^2 - 6400 cm^2

d^2 = 83600 cm^2

Taking the square root of both sides, we find:

d ≈ √83600 cm

d ≈ 289 cm

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Answer:

y = 3

Step-by-step explanation:

Find the difference between the y coordinates, Δy is change in y

Δy = y2 - y1

Find the difference between the x coordinates, Δx is change in x

Δx = x2 - x1

Divide Δy by Δx to find slope

m = Δy/Δx

Example: Find the Slope

Say you know two points on a line and their coordinates are (2, 5) and (9, 19). Find slope by finding the difference in the y points, and divide that by the difference in the x points.

The difference between y coordinates Δy is

Δy = y2 - y1

Δy = 19 - 5

Δy = 14

The difference between x coordinates Δx is

Δx = x2 - x1

Δx = 9 - 2

Δx = 7

Divide Δy by Δx to find slope m

m=142

m=7

Line Equations with Slope

There are 3 common ways to write line equations with slope:

Point slope form

Slope intercept form

Standard form

Point slope form is written as

y - y1 = m(x - x1)

Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point slope form.

Lets use a point from the original example above (2, 5), and the slope which we calculated as 7. Put those values in the point slope format to get an equation of that line in point slope form:

y - 5 = 7(x - 2)

If you simplify the point slope equation above you get the equation of the line in slope intercept form.

Slope intercept form is written as

y = mx + b

Take the point slope form equation and multiply out 7 times x and 7 times 2.

y - 5 = 7(x - 2)

y - 5 = 7x - 14

Continue to work the equation so that y is on one side of the equals sign and everything else is on the other side.

Add 5 to both sides of the equation to get the equation in slope intercept form:

y = 7x - 9

Standard form of the equation for a line is written as

Ax + By = C

You may also see standard form written as Ax + By + C = 0 in some references.

Use either the point slope form or slope intercept form equation and work out the math to rearrange the equation into standard form. Note that the equation should not include fractions or decimals, and the x coefficient should only be positive.

Slope intercept form: y = 7x - 9

Subtract y from both sides of the equation to get 7x - y - 9 = 0

Add 9 to both sides of the equation to get 7x - y = 9

Slope intercept form y = 7x - 9 becomes 7x - y = 9 written in standard form.

Find Slope From an Equation

If you have the equation for a line you can put it into slope intercept form. The coefficient of x will be the slope.

Example

You have the equation of a line, 6x - 2y = 12, and you need to find the slope.

Your goal is to get the equation into slope intercept format y = mx + b

Start with your equation 6x - 2y = 12

Add 2y to both sides to get 6x = 12 + 2y

Subtract 12 from both sides of the equation to get 6x - 12 = 2y

You want to get y by itself on one side of the equation, so you need to divide both sides by 2 to get y = 3x - 6

This is slope intercept form, y = 3x - 6. Slope is the coefficient of x so in this case slope = 3

How to Find the y-Intercept

The y-intercept of a line is the value of y when x=0.  It is the point where the line crosses the y axis.

Using the equation y = 3x - 6, set x=0 to find the y-intercept.

y = 3(0) - 6

y = -6

The y-intercept is -6

How to Find the x-Intercept

The x-intercept of a line is the value of x when y=0.  It is the point where the line crosses the x axis.

Using the equation y = 3x - 6, set y=0 to find the x-intercept.

0 = 3x - 6

3x = 6

x = 2

The x-intercept is 2

Slope of Parallel Lines

If you know the slope of a line, any line parallel to it will have the same slope and these lines will never intersect.

Slope of Perpendicular Lines

If you know the slope of a line, any line perpendicular to it will have a slope equal to the negative inverse of the known slope.

Perpendicular means the lines form a 90° angle when they intersect.

Say you have a line with a slope of -4. What is the slope of the line perpendicular to it?

First, take the negative of the slope of your line

-(-4) = 4

Second, take the inverse of that number. 4 is a whole number so its denominator is 1. The inverse of 4/1 is 1/4.

The negative inverse of a slope of -4 is a slope of 1/4.

A line perpendicular to your original line has a slope of 1/4.

This is just what I think, it might not be right- the first one is (-2, 4), the second one is (-5, 1), the third one is (-2, -2), and the fourth one is (1, 1).

(Sorry if it's wrong-)

Answer: D

Step-by-step explanation:

Answer:

18.25

Step-by-step explanation:

Add 5.50 and 12.75

5.50 + 12.75 = 18.25

Answer: 18.25

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

We can solve this problem by recognizing that z is the geometric mean of 9 and 9+4. This property is outlined in the following formula:

\(\frac{hypotenuse}{leg}=\frac{leg}{part}\)

where hypotenuse is the longest side of the triangle, leg is the side of the triangle we are calculating for, and part is the part of the hypotenuse on the side of the leg.

Here, the hypotenuse is 13, or 4 + 9. The leg is z, as it is the side of the triangle we are trying to find. Finally, the part is 9. It is the part of the hypotenuse that is on the side of the leg.

Let's plug in these values:

\(\frac{13}{z}=\frac{z}{9}\\117=z^2\\z=\sqrt{117}\)

117 is the product of 9 and 13. Since 9 is a perfect square, we can take it out from the square root.

\(z=\sqrt{9*13}\\z=\sqrt{9}*\sqrt{13}\\z=3\sqrt{13}\)

The "?" must be a 3.

Thus, we have proved that for all integers a, b, and c, if a|bc, then a|b or a|c.

To prove that for all integers a, b, and c, if a|bc, then a|b or a|c, we need to use the definition of divisibility.

Assume that a|bc. This means that there exists an integer k such that bc = ak.

We can consider two cases:

Case 1: a and b are coprime.
In this case, a does not share any factors with b. Therefore, a cannot divide b. However, since a|bc and b and c share no factors, a must divide c. Hence, a|c.

Case 2: a and b have a common factor.
In this case, we can write a = dx and b = dy, where d is the greatest common divisor of a and b. Therefore, bc = dxy*c = ak = dxy*k.
Dividing both sides by dxy, we get c/k = a/dy.

Since a and d share no factors, d|c/k. Therefore, there exists an integer m such that c/k = dm. This means that c = dkm.

Since a = dx, we have a|dxk. Since a|bc = dxy*k, we have d|a and d|k. Therefore, we can write k = dh and a = dg, where h and g are integers.

Substituting these expressions into c = dkm, we get c = dg*dh*m. Since d|c and d|a, we have d|b and a|b.

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We have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10.

To quantify the probability of each event, we can define the following events:

Then, the probability of event A is 1/5, since 1 in every 5 units of product A is defective. Similarly, the probability of event B is 1/10, since 1 in every 10 units of product B is defective.

Now, let's consider a scenario where the company receives an order for 100 units of products, with 60 units of product A and 40 units of product B. The company wants to determine the probability of the following events:

To calculate the probability of event C, we need to consider the probability of selecting a defective unit from product A and from product B, and the proportion of each product in the order. Since the order has 60 units of product A and 40 units of product B, the probability of selecting a unit of product A is 60/100 = 3/5, and the probability of selecting a unit of product B is 40/100 = 2/5.

Using the probabilities of event A and event B, we can calculate the probability of selecting a defective unit from product A or from product B as follows:

Therefore, the probability of event C can be calculated as follows:

P(C) = P(A) * P(A in order) + P(B) * P(B in order)

= (1/5 * 3/5) + (1/10 * 2/5)

= 3/25

So the probability of selecting a defective unit from the order is 3/25.

To calculate the probability of event D, we can use the complement rule, which states that the probability of an event and its complement (i.e., the event not happening) add up to 1. Therefore, the probability of event D can be calculated as follows:

P(D) = 1 - P(C)

= 1 - 3/25

= 22/25

So the probability of selecting a unit from the order at random and finding that it is not defective is 22/25.

In summary, we have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10. We have also calculated the probability of two other events (event C and event D) in a scenario where a manufacturing company produces two types of products, with different probabilities of defects, and receives an order with a certain proportion of each product.

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The greatest common factor of a polynomial is the largest expression that divides all of the terms of the polynomial. In this case, we have:

First, find the GCF of the coefficients of the terms. The coefficients are 2, 14 and 6, their GCF is 2.

On the other hand, notice that the factor (c+y) is a common factor for all three terms. Find the greatest power of (c+y) that divides all the terms. Since the lowest power of (c+y) in the expression is 2, then, the greatest power of (c+y) that divides all the terms is (c+y)^2.

The GCF of the expression is the product of the GCF of the coefficients and the GCF of the factors with variables.

Then, the GCF of the expression is:

Factor out 2(c+y)^2 from the expression:

Therefore, the answer is option A and the expression inside the box should be:

The perimeter of the Christian's sandbox is 24 feet.

The given two quadrialterals are similar

Let us find the remaining lengths of Christian's sandbox

By proportional equation

36/8=18/x=27/y=18/z

4.5=18/x=27/y=18/z

x=18/4.5 = 4

y=27/4.5 = 6

z=4

The perimeter is sum of all the sides

So perimeter of Christian's sandbox is 8+6+4+4

24 feet

Hence, the perimeter of the Christian's sandbox is 24 feet.

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Answer:

C. When they're done, José always fills the gas tank.

The greatest number of large pizzas that can be made with the leftover dough is 93.

To determine the greatest number of large pizzas that can be made after lunch with the leftover dough, we first need to calculate the total amount of dough used during lunch.

For small pizzas:

The shop makes 33 small pizzas, and each requires 4 ounces of dough.

Total dough used for small pizzas = 33 pizzas × 4 ounces/pizza = 132 ounces.

For large pizzas:

The shop makes 14 large pizzas, and each requires 4 ounces of dough.

Total dough used for large pizzas = 14 pizzas × 4 ounces/pizza = 56 ounces.

Now, let's calculate the total dough used during lunch:

Total dough used = Total dough used for small pizzas + Total dough used for large pizzas

Total dough used = 132 ounces + 56 ounces = 188 ounces.

Since there are 16 ounces in a pound, we can convert the total dough used to pounds:

Total dough used in pounds = 188 ounces / 16 ounces/pound = 11.75 pounds.

Therefore, the total amount of dough used during lunch is 11.75 pounds.

To find the leftover dough after lunch, we subtract the amount used from the initial amount of dough:

Leftover dough = Initial dough - Total dough used during lunch

Leftover dough = 35 pounds - 11.75 pounds = 23.25 pounds.

Now, we can calculate the maximum number of large pizzas that can be made with the leftover dough:

Number of large pizzas = Leftover dough / Amount of dough per large pizza

Number of large pizzas = 23.25 pounds / 4 ounces/pizza

Number of large pizzas = (23.25 pounds) / (1/4) pounds/pizza

Number of large pizzas = 23.25 pounds × 4 pizzas/pound

Number of large pizzas = 93 pizzas.

Therefore, the greatest number of large pizzas that can be made with the leftover dough is 93.

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a) 19

b) -12

c) 15

d) 18

e) 31

¡Espero que esto te ayude! Avísame si tengo algo mal :)

For Pearson correlation the most common purpose to examine is given by option a. The relationship between 2 variables.

The Pearson correlation is a statistical measure that indicates the extent to which two continuous variables are linearly related.

It measures the strength and direction of the relationship between two variables.

Ranging from -1 perfect negative correlation to 1 perfect positive correlation.

And with 0 indicating no correlation.

It is commonly used in research to examine the association between two variables.

Such as the relationship between height and weight, or between income and education level.

Therefore, the most common purpose of a Pearson correlation is to examine the relationship between 2 variables.

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The above question is incomplete, the complete question is:

The most common purpose for a Pearson correlation is to examine,

a. The relationship between 2 variables

b. Relationships among groups

c. Differences between variables

d. Differences between two or more groups

Answer:

6:1

Step-by-step explanation:

The ratio 12/2 is equivalent to the ratio 6/1, or 12:2 = 6:1 .

To find f'(t), the derivative of the function f(t) = (t^2 + 7t + 7)(6t^2 + 2), we can use the product rule of differentiation.

The product rule states that the derivative of the product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.

Let's differentiate each term separately:

f(t) = (t^2 + 7t + 7)(6t^2 + 2)

f'(t) = (2t + 7)(6t^2 + 2) + (t^2 + 7t + 7)(12t)

Expanding and simplifying:

f'(t) = 12t^3 + 4t + 42t^2 + 14t + 12t^2 + 4t + 42t + 14

Combining like terms:

f'(t) = 12t^3 + 54t^2 + 56t + 14

Therefore, the derivative of f(t) is f'(t) = 12t^3 + 54t^2 + 56t + 14.

To find f'(1), we substitute t = 1 into the derivative:

f'(1) = 12(1)^3 + 54(1)^2 + 56(1) + 14

= 12 + 54 + 56 + 14

= 136

Therefore, f'(1) = 136.

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National income increases, causing interest rates to increase - A) demand for loanable funds shifts outward.

Expansionary fiscal policy does not increase output, it only increases interest rates - E) the IS curve shifts outwards while the LM curve is vertical.

Nominal wages grow faster than the price level - B) real wages increase.

Firms become more confident about the future - D) the demand for money decreases and interest rates decrease.

Credit cards are introduced into the economy - C) the demand for money increases.

When national income increases, it leads to an outward shift in the demand for loanable funds, resulting in increased interest rates. This is because higher national income implies a greater demand for borrowing and investment, leading to increased demand for loanable funds.

Expansionary fiscal policy, which involves increasing government spending or reducing taxes, can lead to an outward shift in the IS curve. However, if the LM curve is vertical, it indicates that the central bank is controlling the money supply to maintain a fixed interest rate. In this case, expansionary fiscal policy will only result in increased interest rates and not increase output.

When nominal wages grow faster than the price level, it leads to an increase in real wages. Real wages refer to wages adjusted for inflation. If nominal wages increase at a faster rate than prices, it means workers have increased purchasing power, resulting in an increase in real wages.

When firms become more confident about the future, it leads to a decrease in the demand for money. Increased confidence encourages investment and spending, reducing the demand for holding money as firms are more willing to invest their funds rather than hold them.

The introduction of credit cards into the economy increases the convenience of transactions and allows individuals to easily access credit. This leads to an increase in the demand for money, as individuals require more money for transactions and credit card payments.

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The random variable x is uniformly distributed between 5 and 19. To compute the standard deviation of x, we can use the formula for the standard deviation of a uniformly distributed continuous random variable:

SD = √[(b - a)^2 / 12]
Here, 'a' represents the lower bound (5) and 'b' represents the upper bound (19). Plugging these values into the formula, we get:
SD = √[(19 - 5)^2 / 12]
SD = √[(14)^2 / 12]
SD = √[196 / 12]
SD = √[16.333]
Therefore, the standard deviation of x is approximately 4.041. The correct answer is option (a) 4.041.

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Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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The correct answer is c. tunnel. A narrow underground excavation with a depth greater than the width, but no wider than 15 is called a tunnel.

Tunnels are commonly used for transportation purposes, such as road or railway tunnels, as well as for utilities like water or sewage systems. They are also used in mining operations to access underground resources.

Tunnels are different from trench excavations, which are narrow excavations that are typically used for utility installations or drainage purposes.

Excavation is a broader term that refers to any process of digging or removing earth or rock.

A borrow pit, on the other hand, is an excavation where soil, sand, or gravel is taken from to be used in construction projects.

So, the correct term for a narrow underground excavation with the given characteristics is a tunnel.

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The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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The result obtained after evaluating the polynomials are :

Given the polynomials :

1) 7x + 2x + 19x

7x + 2x + 19x = 28x

2) -6x - 3 + 3x - 9

-6x + 3x - 3 - 9

= -3x - 9

3) (3x-4y) - (x+2y)

3x - 4y - x - 2y

3x - x - 4y - 2y

= 2x - 6y

4) 18x5 - 6x3

= 18x^5 - 6x³

5) (x+5)(x-7)

Expand

x² - 7x + 5x - 35

x² - 2x - 35

Therefore, the simplified expression for the polynomials are given above.

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Answer:

16.97km

Step-by-step explanation:

To get the displacement, we will use the pythagoras theorem

Sum of distances along the horizontal (east and west) is expressed as

dx = 10 - 4 + 6

dx = 6+6

dx = 12km

Sum of distances along the y;

dy = 2 - 13 - 1

dy = -11-1

dy = -12km

Find the displacement using the pythagoras theorem

D = √(12)²+(-12)²

D = √144+144

D = √288

D = 16.97km

Hence her displacement is 16.97km

Answer:

Step-by-step explanation:

Answer: A

Step-by-step explanation:

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