5. Patsy is getting supplies for her daughter's birthday party. She's getting special large balloons (b) that are $3 each and unicorn headbands (h) that are $5 each. Patsy spends $61 for the balloons and headbands. a. Write an equation in standard form to represent the situation. b. There are going to be 8 girls (including her daughter) at the party. Each girl gets one unicorn headband. How many balloons did Patsy buy?​

We can estimate that approximately 35 gas stations sell a gallon of regular gas for no more than $2.01.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". The percentage can be calculated by dividing the value by the total value and then multiplying the result by 100.

a) To find the percentage of gas stations that sell regular gas for less than $1.973, we need to calculate the z-score corresponding to this value:

z = (1.973 - 2.05) / 0.47 = -0.164

Using a standard normal distribution table or calculator, we can find that the percentage of gas stations selling regular gas for less than $1.973 is approximately 44.38%.

b) To find the percentage of gas stations selling regular gas for at least $2.17, we can calculate the z-score corresponding to this value:

z = (2.17 - 2.05) / 0.47 = 0.255

Using a standard normal distribution table or calculator, we can find that the percentage of gas stations selling regular gas for at least $2.17 is approximately 40.86%.

c) To find the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05, we can calculate the z-scores for each value:

z1 = (1.97 - 2.05) / 0.47 = -0.164

z2 = (2.05 - 2.05) / 0.47 = 0

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to each z-score:

P(z < -0.164) = 0.4364

P(z > 0) = 0.5 - 0.5(0) = 0.5

To find the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05, we can add these probabilities:

P(z < -0.164 or z > 0) = P(z < -0.164) + P(z > 0) = 0.4364 + 0.5 = 0.9364

Therefore, the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05 is approximately 93.64%.

d) To find the number of gas stations that sell regular gas for no more than $2.01, we can calculate the z-score corresponding to this value:

z = (2.01 - 2.05) / 0.47 = -0.085

Using a standard normal distribution table or calculator, we can find the probability corresponding to this z-score:

P(z < -0.085) = 0.4664

Multiplying this probability by the total number of gas stations (75), we can estimate the number of gas stations that sell regular gas for no more than $2.01:

0.4664 * 75 ≈ 35

Therefore, we can estimate that approximately 35 gas stations sell a gallon of regular gas for no more than $2.01.

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Complete question:

The price of a gallon of regular gasoline at 75 What percent of gasoline gas stations sell gallons of gas stations across the state is normally regular gas for less than $1.973 distributed with & a mean of $2.05 and a standard deviation of 47. b) What percent of gas stations sell a gallon? regular gas for at least $2.17? c) What is The probability that gas station sells gallons of regular gas for less than $1.97 or greater than $2.05? About how many stations sell a gallon of regular gas for no more than $2.01?

(a) The expected profit of this policy to the insurance company is $520.10.

(b) The interpretation value of expected profit in (a) in the context of the problem is small probability of the policyholder's death.

(a) The expected profit to the insurance company can be calculated as follows:

Expected Profit = (Probability of Survival * Premium) - (Probability of Death * Death Benefit)

Probability of Survival = 0.997

Probability of Death = 1 - Probability of Survival = 1 - 0.997 = 0.003

Premium = $780

Death Benefit = $250,000

Expected Profit = (0.997 * $780) - (0.003 * $250,000) = $520.10

Therefore, the expected profit to the insurance company from selling this policy is $520.10.

(b) The expected profit of $520.10 represents the average profit that the insurance company can expect to earn from selling this type of policy to similar customers over time.

In the context of this problem, it means that if the insurance company sells many policies like this one, they can expect to make a profit of about $520.10 per policy, on average, after accounting for the small probability of the policyholder's death.

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The the rectangular prisms have their volumes as:

1). 175 cubic feet

2). 60 cubic metres

3). 140 cubic metres

4). 216 square inches.

volume for a rectangular prism is calculated using:

length × width × height

the rectangular prisms can be divided into bigger and smaller prism and their volumes calculated separately and then added to get the total volume as follows:

1). volume of bigger rectangular prism = 7ft × 7ft × 3ft = 147ft³

volume of smaller rectangular prism = 7ft × 2ft × 2ft = 28ft³

volume of object = 147ft³ + 28ft³ = 175ft³

2). volume of bigger rectangular prism = 6m × 3m × 3m = 54m³

volume of smaller rectangular prism = 3m × 3m × 1m = 6m³

3). volume of bigger rectangular prism = 7m × 6m × 3m = 126m³

volume of smaller rectangular prism = 7m × 2m × 1m = 14m³

volume of object = 126m³ + 14m³ = 140m³

4). volume of bigger rectangular prism = 12in × 4in × 4in = 192in²

volume of smaller rectangular prism = 4in × 3in × 2in = 24in³

volume of object = 192in³ + 24in³ = 216³

Therefore, the rectangular prisms have their volumes as:

1). 175 cubic feet

2). 60 cubic metres

3). 140 cubic metres

4). 216 square inches

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To determine whether the relation is a function, we need to check if each x-value is associated with only one y-value in the mapping diagram.

A mapping diagram is a picture of two circles that shows the connection between input and output values. Illustration of a mapping diagram. The x-values (inputs) in the image are converted to the associated y-values by drawing an arrow from one x-value to its corresponding y-value (outputs).

From the given mapping diagram, we can see that the x-value -8 is associated with the y-value -4, the x-value -5 is associated with the y-value -2, the x-value -1 is associated with the y-value -2, the x-value 1 is associated with the y-value -2, the x-value 12 is associated with both the y-value -4 and -2.

Since the x-value 12 is associated with two different y-values, the given relation is not a function. To be a function, each x-value must be associated with only one y-value in the mapping diagram.

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Answer: I think its C lmk if I'm wrong

Explanation:

Integral is a mathematical concept that is used to calculate the area under a curve between two points or to find the total accumulation of a quantity over a given interval.

The integral of a function is represented by the symbol ∫ and is also known as the "antiderivative" or "primitive" of the function. It is the opposite of the derivative operation, which finds the rate of change of a function at a given point. Instead, the integral finds the original function whose derivative is the given function.

The process of finding the integral of a function is called integration, and it involves summing up an infinite number of small areas under the curve of the function. The result of the integration is a new function that represents the area under the curve of the original function between the given limits of integration. It is an important tool in calculus and is used to solve a wide range of mathematical problems.

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The value of 0.4375 in fractional form is 7/16.

Parts of a whole numbers are represented by fractions, where the denominator represents the entire object and the numerator the equal part.

By dividing a number by 10 for each digit after the decimal, we may eliminate the decimal and turn it into a fraction.

The decimal point is followed by four integers, thus we will divide it by 10,000.

= 4375 / 10000

Simplifying fraction yields the result

= 4375 ÷ 5 / 10000 ÷ 5

= 875 ÷ 5 / 2000 ÷ 5

= 175 ÷ 5 / 400 ÷ 5

= 35 ÷ 5 / 80 ÷ 5

= 7 / 16

In addition, they are comparable fractions.

The fractional equivalent of 0.4375 is 7/16.

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Complete question - what is 0.4375 as a fraction?

Answer:

I don’t understand

Step-by-step explanation:

I had the same one

The actual size of 2×4 is 1.5 inches by 3.5 inches

The measurement is 2 × 4

Assuming you are referring to lumber sizes, a 2x4 piece of lumber has actual dimensions of 1.5 inches by 3.5 inches

If we convert to the centimeter then the actual size will be 3.81 cm by 8.89 cm

The name "2x4" refers to the rough dimensions of the lumber before it is planed and smoothed, which are typically about 2 inches by 4 inches. However, the planing process reduces the size of the lumber by about 0.5 inches in both dimensions.

Therefore, the actual size is 1.5 inches by 3.5 inches

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The method to convert mililitres to litres is the formula - Quantity in litres = quantity in mililitres/1000.

Remember that ml is the unit of volume which is abbreviated to mililitres. Now, going to the relation between mililitres and litres. We are aware that 1 litre is equal to 1000 mililitres. So, converting mililitres to litres, we need to use the following formula -

Quantity in litres = quantity in mililitres/1000

Using an example to verify the mentioned relation. Let us say we have 4000 mililitres of acid. So, what will be the volume of acid in litres.

Quantity of acid in litres = 4000/1000

Performing division

Quantity of acid in litres = 4 litres

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89 centimeter is approximately equal to 35.0394 inches ( rounded to four decimal places )

To convert 89 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

89 cm = 89 x 0.393701

Multiply the numbers

= 35.0394 inches ( rounded to four decimal places )

Therefore, 89 centimeter is 35.0394 inches

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The image of vertex Z after a 90 degree counterclockwise rotation about the origin is (-34, -1). To find the coordinates of the image points for X and Y, we would need to know their coordinates as well.

Although the question is a little challenging to understand as worded, I'll do my best to respond.

Here is what I believe you are asking, assuming "verticals eggs" is a typo and you meant "vertex angles" and "Z bar" is a typo and you meant "Z = (-1, 34)":

Triangle XYZ has vertex angles at X and Y and vertices at X, Y, and Z. Pointed at is Vertex Z (-1, 34). What are the coordinates of the picture points for the triangle XYZ if the triangle is rotated 90 degrees anticlockwise about the origin?

We can use the following rotation matrix to rotate the origin 90 degrees anticlockwise:

R = [sin(90); cos(90); cos(90)-cos(90)]

R = [0 -1; 1 0]

We may represent the coordinates of each point in the triangle as a column vector and then multiply by the rotation matrix to apply this matrix to each point in the triangle:

[X'; Y'] = R * [X; Y]

[Z'] = R * [Z; 1]

(Notice that we make the Z coordinate a homogeneous coordinate by adding a third component of 1 to it.)

We are unable to provide the precise coordinates of the image points without knowing the X and Y coordinates. However, we can multiply matrices using the Z coordinate that is provided:

[Z'] = R * [-1; 34; 1]

[Z'] = [(-1) * 0 + 34 * (-1) + 1 * 0; (-1) * 1 + 34 * 0 + 1 * 0; (-1) * 0 + 34 * 0 + 1 * 1]

[Z'] = [-34; -1; 1]

Hence, vertex Z's image following a 90° anticlockwise rotation of the origin is (-34, -1). We would also need to know their coordinates in order to determine the coordinates of the image points for X and Y.

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The value of z is given as follows:

z = 3.5.

Similar triangles are triangles that share these two features presented as follows:

Considering that the two triangles in this problem are similar, the proportional relationship for the side lengths is given as follows:

z/7  =3/6 = 1/2.

Hence:

z/7 = 1/2.

Applying cross multiplication, the value of z is given as follows:

2z = 7

z = 7/2

z = 3.5.

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3.5 kg is approximately equal to 7.7162 pounds ( rounded to four decimal places )

The conversion factor to convert kg to pounds is 2.20462

1 kg = 2.20462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in pounds = The mass in kg × conversion factor

Substitute the values in the equation

1 kg = 2.20462 pounds

3.5 kg =  3.5 × 2.20462

Multiply the numbers

= 7.7162 pounds  ( rounded to four decimal places )

Therefore, 3.5 kg is 7.7162 pounds

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Option A. 57. Roman numerals use letters from the Latin alphabet to represent numbers. The Roman numeral LVII represents the number 57.

The basic symbols used in the Roman numeral system are I, V, X, L, C, D, and M, which represent the numbers 1, 5, 10, 50, 100, 500, and 1,000, respectively. By combining these symbols, larger numbers can be formed.

In the case of LVII, the symbol L represents 50, the symbol V represents 5, and the symbol II represents 2. To get the total value of the Roman numeral, we add up the values represented by each symbol. So:

LVII = L + V + II

= 50 + 5 + 2

= 57

Therefore, the Roman numeral LVII represents the number 57.

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What number does the roman numeral LVII represent?

A. 57

B. 58

C. 59

D. 60

Mr. Davis' granola snacks will last for 20 days.

What is division ?

Division is a basic arithmetic operation used to find the quotient or the number of times one quantity is contained within another. In division, a dividend is divided by a divisor, and the result is the quotient. For example, 12 divided by 3 is 4, where 12 is the dividend, 3 is the divisor, and 4 is the quotient.

Division is the inverse operation of multiplication. If you know the multiplication facts, you can use them to help you divide numbers. For instance, if you know that 5 times 6 equals 30, then you also know that 30 divided by 5 equals 6, and that 30 divided by 6 equals 5.

According to given conditions:

To find out how many days Mr. Davis' granola snacks will last, we need to divide the total amount of granola by the amount he eats each day.

Let's say Mr. Davis made 10 lbs of granola snacks.

He eats 0.5 lb each day.

So we can use the formula:

Number of days = Total amount of granola / Amount eaten each day

Number of days = 10 lbs / 0.5 lb per day

Number of days = 20 days

Therefore, Mr. Davis' granola snacks will last for 20 days.

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The table representing the relationship between hours of lawn care and the amount of money the company charges is:

8 $220

10 $275

12 $330

14 $385.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) symbol on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS (left hand side equals right hand side) is the most widely accepted theorem.

Let x be the charge of lawn care for 1 hour.

Given, charge for 4 hours of lawn care =$110

So, x= Amount charged/ Hours of lawn care

x=110/4

x=27.5

Now, the company charges $27.5 for 1 hour of lawn care.

So now we can find the amount charged by the company for

"y" no. of hours by using the equation. x × y = z

Here x, y and z are variables, where x is the charge of lawn care for 1 hour. y is the number of hours of lawn care and z is the total amount

charged by the company.

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Regression line is used to make predictions about the values of y for a given x-value and to determine the strength of a linear association between two variables. The correct answer is option D.

The regression line is a straight line that best represents the relationship between two variables. It is commonly used in statistics and data analysis to make predictions about one variable based on the other variable. The regression line can also be used to determine the strength of the linear association between the two variables.

Option A is correct because the regression line can be used to make predictions about the values of y for a given x-value. Once the regression line has been calculated, it can be used to estimate the value of y for any given value of x. This is particularly useful in situations where it is not feasible or practical to obtain the actual value of y for a given x.

Option B is also correct because the regression line provides a measure of the strength of the linear association between two variables. The slope of the regression line indicates the direction and strength of the relationship between the two variables.

A positive slope indicates a positive relationship, while a negative slope indicates a negative relationship. The closer the slope is to zero, the weaker the relationship between the two variables. Therefore, Correct option is D - Both A and B.

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86 inches are equivalent to 7.17 feet

To convert inches to feet, you can divide the number of inches by 12 (since there are 12 inches in a foot):

86 inches ÷ 12 inches/foot = 7.17 feet

The units of measurement used to measure length or distance are inches and feet. One inch is equivalent to one-twelfth of a foot, while one foot is equal to twelve inches. As a result, you may easily convert feet to inches by multiplying the number of feet by 12. 36 inches, for instance, is equivalent to 3 feet (3 feet x 12 inches/foot).

Divide the number of inches by 12 to convert the measurement to feet. As an illustration, 24 inches (12 inches per foot) equals 2 feet.

Inches and feet are often used to measure an object's height, breadth, and length in the United States.

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A quart contains 32 ounces. This is true for both dry and liquid ounces.

In the United States, the conventional system of measurement—in which dry measurements are reported in weight ounces and volume measurements are given in fluid ounces—is frequently employed. Four cups, two pints, or 32 fluid ounces make up a quart.

It's crucial to keep in mind that the density of a component might affect how much an ounce weighs when weighing dry ingredients.

For instance, due to the difference in their densities, one fluid ounce of flour will weigh less than one fluid ounce of sugar. Nonetheless, regardless of the density, each fluid ounce has a standard weight when measuring volume using fluid ounces.

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The question is -

what are ounces in a quart?

The vertex is (-1, -6) and the axis of symmetry is -1. The function is minimum. The solution has been obtained by using equation of parabola.

What is a parabola?

Any point on a parabola is equally separated from both the focus, or predetermined point, and the fixed straight line (known as the directrix).

We are given f(x) = 2(x + 1)² - 6

We know that a parabola of equation a(x - h)² + k always has its vertex at (h, k) with axis of symmetry at x = h.

So, the vertex here is (-1, -6) and the axis of symmetry is x = -1.

It is a minimum function because there is a positive value before (x - h)².

Hence, the vertex is (-1, -6) and the axis of symmetry is -1 and the function is minimum.

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The congruence rule is the ASA (Angle-Side-Angle) rule of congruence

The triangle EFD is congruent to triangle STR.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

Here, we have,

In the figure shown:

The side FD= RT belong to both △EFD and △STR

Since the two triangles, △EFD and △STR, have two congruent angles and an included side,  △EFD and △STR are congruent according to the ASA rule.

The ASA rule states that if two angles and an included side of one triangle are congruent to the two angles and an included side of another triangle, then the two triangles are also congruent.

Hence, The congruence rule is the ASA (Angle-Side-Angle) rule of congruence. The triangle EFD is congruent to triangle STR.

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five-ninths times four equals two and two-ninths.

What is an Algebraic Expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.

For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.

In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.

Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations

To solve five-ninths times four, we multiply 5/9 by 4, which gives:

5/9 x 4 = 20/9

So, the expression "five-ninths times four" is equal to 20/9.

Out of the options given, the answer closest to 20/9 is "two and two-ninths," which can be written as 20/9. Therefore, the answer is:

Therefore, five-ninths times four equals two and two-ninths.

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Answer:

Step-by-step explanation:  15 feet of the ladder will be under the water because at first the ladder was 10 feet long then it  rises from under water

Answer:

The cost of the computer is 712 and the cost of the printer is 350. This can be calculated by setting up a simple equation: x + 2x = 1062, where x is the cost of the printer. Solving for x gives x = 350, which means that the cost of the printer is 350 and the cost of the computer is 2x = 2(350) = 712.

The variance for the sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores is 5.

The formula for the variance of a sample is:

[tex]s^2[/tex] = SS / (n - 1)

where SS is the sum of squared deviation scores, n is the sample size, and [tex]s^2[/tex] is the variance.

In this case, SS = 20 and n = 5, so we can substitute these values into the formula:

[tex]s^2[/tex] = 20 / (5 - 1)

[tex]s^2[/tex] = 5

Therefore, the variance for this sample is 5.

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Answer:

8/100 or 2/25

Step-by-step explanation:

The decimal 0.08 can be written as the fraction 8/100 or, in simplest form, 2/25.

The area of the purple ring is 10,843.079 ft²

Remember that for a circle of radius R the circumfernce is:

C = 2*3.14*R

Here we know that the circumference of the inner circle is C = 221.056 ft

Then the radius will be:

221.056 ft = 2*3.14*R

221.056 ft/(2*3.14) = R

35.2 ft = R

Then the radius of the outer circle is:

R' = 35.2ft + 33.3ft = 68.5 ft

The area of the ring is the diffence between the areas of the larger circle and the smaller circle, then:

area = 3.14*( (68.5 ft)² - (35.2 ft)²) = 10,843.079 ft²

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Answer:
Unit Rate: $10/km

Equation: x=y/10 or y=10x

The Olson family drinks milk at a rate of 1/6 gallon per day.

To find the rate at which the Olson family drinks milk, we need to divide the amount of milk they drink by the time it takes them to drink it.

They use up a 1/2-gallon jug every 3 days, so their rate of milk consumption is:

(1/2 gallon) ÷ (3 days) = 1/6 gallon per day

A gallon is a unit of volume measurement commonly used in the United States and some other countries. There are different types of gallons, but the most commonly used ones are:

US liquid gallon (abbreviated as "gal" or "US gal"): This is a unit of volume used for measuring liquid substances. It is defined as exactly 3.785411784 liters or approximately 0.83267418 Imperial gallons.

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