When the weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs then the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.
The weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs.
We need to find the z-score corresponding to a little boy's weight of 33 lbs.
The z-score measures the number of standard deviations an observation is from the mean of a distribution.
It helps in determining the relative position of a value within a distribution.
To calculate the z-score, we use the formula:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.
In this case, the observed weight is 33 lbs, the mean is 21 lbs, and the standard deviation is 0.7 lbs.
Substituting these values into the formula, we get:
z = (33 - 21) / 0.7
Calculating the numerator, we have:
z = 12 / 0.7
Simplifying further, we get:
z ≈ 17.14
Therefore, the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.
This indicates that the weight of the little boy is about 17.14 standard deviations above the mean weight of 3-year-old boys.
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In ΔABC, the measure of ∠C=90°, the measure of ∠A=5°, and BC = 3 feet. Find the length of CA to the nearest tenth of a foot
Select each expression that has a value of 15 when x = 15 D A - 10 3 DB 15.521 * * OC (3,015 - ) - 186 OD 2022-30 DE -25 what is the answer?
The expressions that have a value of 15 when x = 15 include the following:
A. x/3 + 10
C. (3,015 ÷ x) - 186
How to evaluate each of the expression?Based on the information provided, we would determine the output value of each of the given expression by substituting 15 for the value of x as follows;
Expression = x/3 + 10
Expression = 15/3 + 10
Expression = 5 + 10
Expression = 15 (True).
Expression = 15,521 ÷ x
Expression = 15,521 ÷ 15
Expression = 1034.73 (False).
Expression = (3,015 ÷ x) - 186
Expression = (3,015 ÷ 15) - 186
Expression = 201 - 186
Expression = 15 (True).
Expression = 20x² ÷ 30
Expression = 20(15)² ÷ 30
Expression = 4500 ÷ 30
Expression = 150 (False).
Expression = 20x²/5 - 25
Expression = 20(15)²/5 - 25
Expression = 900 - 25
Expression = 875 (False).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the tax amount given the original price and the tax rate. Round to the nearest cent if necessary. Original price: $58.73 Tax: 6.5%
The tax amount, rounded to the nearest cent, is approximately $3.81.
To find the tax amount given the original price and the tax rate, we can multiply the original price by the tax rate.
Original price: $58.73
Tax rate: 6.5%
To calculate the tax amount, we need to convert the tax rate from a percentage to a decimal by dividing it by 100:
Tax rate = 6.5% = 6.5/100 = 0.065
Now we can calculate the tax amount by multiplying the original price by the tax rate:
Tax amount = $58.73 * 0.065
Tax amount ≈ $3.81 (rounded to the nearest cent)
Therefore, the tax amount, rounded to the nearest cent, is approximately $3.81.
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Three people share seven brownies. How many brownies should each person get?
Three people share seven brownies. Each person should get 2 brownies since 2 is the closest value that is less than 2.33 since the answer should be a whole number.
Explanation: We can calculate the number of brownies each person should get by dividing the total number of brownies by the number of people that will share them. Since three people are to share 7 brownies, we divide 7 by 3.Thus, each person should get 2 and 1/3 of a brownie. This value, however, cannot be the answer since it should be a whole number. Therefore, we take the closest b number that is less than 2.33, which is 2. This implies that each person should get 2 brownies.
In essence, we will have shared 6 brownies since 2 x 3 is equal to 6. So, one brownie will be left. This means that the brownie should be shared among the three people. Each person will receive two brownies and the remaining one brownie should be shared equally among the three. So, each person should get two and one-third pieces of brownies.
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Determine the period. Acellus
Answer: 15
Step-by-step explanation:
Period=distance between 2 top points.
15
Farid has two types of sticks: short ones, measuring 1 cm and long ones, measuring 3 cm. With which of the combinations below can he make a square, without breaking or overlapping the sticks?
Farid can make a square by using a combination of two short sticks and two long sticks.
To form a square without breaking or overlapping the sticks, the length of each side of the square must be equal. In this case, we have two types of sticks: short ones measuring 1 cm and long ones measuring 3 cm.
To determine which combinations can form a square, we need to consider the lengths of the sides and the total length of the sticks.
1. Using only short sticks (1 cm each):
To form a square, we need four equal sides. Since each short stick measures 1 cm, the total length of the four sides would be 4 cm. This combination does not work as the total length is too small to form a square.
2. Using only long sticks (3 cm each):
Similarly, using only long sticks would result in a total length of 12 cm for the four sides. This combination also does not work as the total length is too large to form a square.
3. Using a combination of short and long sticks:
In this case, we can combine short and long sticks to create a square. For example, using two short sticks and two long sticks would give us a total length of 2 cm + 2 cm + 3 cm + 3 cm = 10 cm. This combination can form a square with each side measuring 2.5 cm.
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What is a positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees and a negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees?
the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.
To find th positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees, and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees,
we can use the following formulas:For a positive coterminal angle, add 360 degrees repeatedly until we reach the desired range.For a negative coterminal angle, subtract 360 degrees repeatedly until we reach the desired range.
Let's start with the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees.
To find this angle, we need to add 360 degrees repeatedly until we reach a value between 500 degrees and 1000 degrees.
So, we can write:47 + 360 = 407 (not in range)
407 + 360 = 767 (not in range)
767 + 360 = 1127 (not in range)
1127 + 360 = 1487 (not in range)
1487 + 360 = 1847 (not in range)
1847 + 360 = 2207 (not in range)
2207 + 360 = 2567 (not in range)
2567 + 360 = 2927 (not in range)
2927 + 360 = 3287 (not in range)
3287 + 360 = 3647 (not in range)
3647 + 360 = 4007 (not in range)
4007 + 360 = 4367 (not in range
4367 + 360 = 4727 (not in range)
4727 + 360 = 5087 (not in range
5087 + 360 = 5447 (not in range
)5447 + 360 = 5807 (not in range)
5807 + 360 = 6167 (not in range)
6167 + 360 = 6527 (not in range)
6527 + 360 = 6887not in range)
6887 + 360 = 7247 (not in range
)7247 + 360 = 7607 (not in range)
7607 + 360 = 7967 (not in range)
7967 + 360 = 8327 (not in range)
8327 + 360 = 8687 (not in range)
8687 + 360 = 9047 (not in range)
9047 + 360 = 9407 (not in range)
9407 + 360 = 9767 (not in range
)9767 + 360 = 10127 (not in range)
10127 + 360 = 10487 (not in range)
10487 + 360 = 10847 (not in range)
10847 + 360 = 11207 (in range)
Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 11207 - 10847 = 360 degrees.
To find the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees, we need to subtract 360 degrees repeatedly until we reach a value between -500 degrees and 0 degrees. So, we can write:
47 - 360 = -313 (not in range)
-313 - 360 = -673 (not in range)
-673 - 360 = -1033 (not in range)
-1033 - 360 = -1393 (not in range
-1393 - 360 = -1753 (not in range)
-1753 - 360 = -2113 (not in range)
-2113 - 360 = -2473 (not in range)
-2473 - 360 = -2833 (not in range
-2833 - 360 = -3193 (not in range
-3193 - 360 = -3553 (not in range)
-3553 - 360 = -3913 (not in range)
-3913 - 360 = -4273 (not in range)
-4273 - 360 = -4633 (not in range)
-4633 - 360 = -4993 (in range)
therefore, the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is -4993 - (-5183) = 190 degrees.
Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.
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your planning w dinner party with the budget of 50$ and a menu that consists of 1 main dish 2 side dish and 1 dessert
This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!
If you're planning a dinner party with a budget of $50 and a menu that consists of 1 main dish, 2 side dishes, and 1 dessert, there are plenty of affordable options you can choose from. Here's a sample menu that should fit within your budget:Main Dish: Baked Chicken - $10Ingredients:4 chicken leg quarters - $6.004 tbsp olive oil - $0.501 tbsp salt - $0.101 tbsp pepper - $0.101 tbsp garlic powder - $0.101 tbsp paprika - $0.10Directions:Preheat oven to 400°F. Combine salt, pepper, garlic powder, and paprika in a small bowl.
Drizzle chicken with olive oil and rub spice mixture onto chicken. Place chicken in a baking dish and bake for 45-50 minutes until chicken is cooked through.
Side Dish 1: Garlic Roasted Potatoes - $4Ingredients:6 medium-sized potatoes - $1.501/4 cup olive oil - $0.751 tbsp salt - $0.101 tbsp pepper - $0.101 tb sp garlic powder - $0.10Directions:Preheat oven to 400°F. Wash potatoes and cut them into small cubes.
Combine potatoes with olive oil, salt, pepper, and garlic powder in a large mixing bowl. Spread the potatoes out in a single layer on a baking sheet and bake for 30-35 minutes until golden brown and crispy.
Side Dish 2: Sauteed Green Beans - $3Ingredients:
1 lb green beans - $2.001/4 cup butter - $0.501 tbsp garlic - $0.101/2 tbsp salt - $0.051/2 tbsp pepper - $0.05Directions:Bring a pot of water to a boil and blanch green beans for 2-3 minutes. Drain and rinse under cold water. Combine flour, rolled oats, brown sugar, butter, cinnamon, and nutmeg in a mixing bowl. Use your hands to mix the ingredients together until crumbly. Spread the topping over the apples and bake for 35-40 minutes until golden brown and crispy.
Total cost: $25This sample menu should feed around 6-8 people, depending on portion sizes. You can adjust the amounts of ingredients as needed to fit your specific needs. You may also be able to find some ingredients on sale or substitute them for cheaper options to save even more money. Happy planning!
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Classify each number according to its value. 4. 2 × 10-6 2. 1 × 10-3 3. 1 × 10-2 3. 2 × 10-5 3. 5 × 10-4 5. 8 × 10-3 5. 2 × 10-4.
The given numbers can be classified into two categories: small values and very small values (closer to zero). All the given numbers have values that are either small or very small, with some being closer to zero than others based on the number of places the decimal point is moved to the left.
In scientific notation, numbers are expressed as a product of a decimal number between 1 and 10, and a power of 10. The power of 10 indicates the number of places the decimal point is moved to the right (if the exponent is positive) or to the left (if the exponent is negative).
Based on the given numbers:
1. 2 × 10^(-6): This number is very small, as the exponent is negative and indicates that the decimal point is moved 6 places to the left.
2. 1 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.
3. 1 × 10^(-2): Similar to the previous number, this is also a small value, with the exponent indicating a movement of 2 places to the left.
4. 2 × 10^(-5): This number is very small, with the exponent indicating a movement of 5 places to the left.
5. 5 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.
6. 8 × 10^(-3): This number is a small value, with the exponent indicating a movement of 3 places to the left.
7. 2 × 10^(-4): This number is a small value, with the exponent indicating a movement of 4 places to the left.
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ALMN, LM || OP. Given that NL=35, NO=20, and NM=49, find NP.
L
O
N
M
NP =
Answer:
NP=28
Step-by-step explanation:
20/35=x/49
cross multiply
35x=20x49
35x=980
x-980/35
x=28
Mr. Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below.Based on this work, what is the solution to the system?(-4, -4)(0, 0)no solutioninfinitely many solutions
The solution to the system of equations is (-4, 4).
The system of equations is: x + y = -8 and x - y = 0
Mr. Brown can find the solution to the system of equations by solving it using the elimination method as follows:
x + y = -8 (Equation 1)
x - y = 0 (Equation 2)
Add Equation 1 and Equation 2.
Doing so will eliminate y from the equations and solve for x.
x + y + x - y = -8 + 0
2x = -8 x = -4
Substitute x = -4 into any of the original equations to solve for y.
Let's use Equation 2: x - y = 0 -4 - y = 0
y = -(-4) y = 4
Therefore, the solution to the system of equations is (-4, 4).
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You pick a card from a standard deck, look at it, then pick a second card. Since a standard deck of 52 cards has 13 hearts and 13
diamonds, is the probability of drawing a heart and then a diamond 13/52 x 13/52
Yes, the probability of drawing a heart and then a diamond from a standard deck of 52 cards is indeed (13/52) x (13/52).
To calculate the probability of two independent events occurring, we multiply their individual probabilities. In this case, the probability of drawing a heart on the first card is 13 out of 52 because there are 13 hearts in a standard deck of 52 cards. The probability of drawing a diamond on the second card is also 13 out of 52 since there are 13 diamonds in the deck.
Therefore, the probability of drawing a heart and then a diamond is:
(13/52) x (13/52) = (169/2704) = 1/16 ≈ 0.0625 ≈ 6.25%
So, the probability of drawing a heart and then a diamond from a standard deck is 13/52 multiplied by 13/52.
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The cost of all your ingredients for your cake is $3. 49. You consistently sell 150 cakes per week for $976 in total sales. What is your food cost percentage?
The cost of ingredients for a cake is $3.49, and the total weekly sales from selling 150 cakes are $976. We will calculate the food cost percentage. The food cost percentage is approximately 35.76%.
To calculate the food cost percentage, we need to determine the portion of the total sales that goes towards the cost of ingredients. The food cost is the cost of ingredients, and the total sales is the revenue generated.
First, we calculate the cost per cake:
Cost per cake = Cost of ingredients / Number of cakes sold
Cost per cake = $3.49 / 150 cakes
Cost per cake ≈ $0.0233
Next, we calculate the total cost of ingredients for all the cakes sold:
Total cost of ingredients = Cost per cake * Number of cakes sold
Total cost of ingredients = $0.0233 * 150 cakes
Total cost of ingredients = $3.495
Now, we can calculate the food cost percentage:
Food cost percentage = (Total cost of ingredients / Total sales) * 100
Food cost percentage = ($3.495 / $976) * 100
Food cost percentage ≈ 0.3576 * 100
Food cost percentage ≈ 35.76%
Therefore, the food cost percentage is approximately 35.76%.
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54 cu. In. 72 cu. In. 36 cu. In. 80 cu. In. Dimensions of Rectangular Prism Volume of Rectangular Prism 4 in. , 3 in. , 6 in. 6 in. , 3 in. , 2 in. 4 in. , 5 in. , 4 in. 2 in. , 9 in. , 3 in.
The dimensions of a rectangular prism can be matched with the volume of the rectangular prism as follows:
4 in., 3 in., 6 in. = 72 in³6 in., 3 in., 2 in. = 36 in³4 in., 5 in., 4 in. = 80 in³2 in., 9 in., 3 in. = 54 in³How to match the dimensions to the volumeTo match the dimensions of the rectangular prism to the volume we need to know the formula or the volume of a rectangular prism. That is;
length * breadth * height.
So, for the dimensions given, we would simply multiply all the side lengths to arrive at the final volume of the rectangular prism. For the first one,
4 * 3 * 6 = 72 in³
6 * 3 * 2 = 36 in³
4 * 5 * 4 = 80 in³
2 * 9 * 3 = 54 in³
The results represent the final volumes of the rectangular prisms.
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PLEASE, I REALLY NEED HELP HOW DO I DO A VERBAL EXPLANATION FOR THIS??? PLEASE
The radical form of[tex](-3x^3)^-^2/3 is 1 / (9x^2)[/tex].
To rewrite the expression[tex](-3x^3)^-^2/3[/tex] as a radical, we can use the fact that a negative exponent indicates that the base is in the denominator. Therefore, we can rewrite the expression as:
[tex]1 / (-3x^3)^(^2^/^3^)[/tex]
Using this concept, we can rewrite the exponent -2/3 as [tex]3\sqrt(1/-3^2)[/tex], where 3√ is the cube root. We also need to take the cube root of the absolute value of -3x^3 to ensure that the result is always positive.
To find the radical form, we can simplify the expression under the radical by raising it to the power of 3/2:
[tex](-3x^3)^(^2^/^3) = [(-3)^(^2^/^3^) * (x^3)^(^2^/^3^)]^3 = [(9 * x^2)^(^1^/^3^)]^3 = 9x^2[/tex]
Substituting this back into the original expression gives:
1 / (-3x^3)^(2/3) = 1 / (9x^2).
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Which statements describe the function f(x) = 3(1/3)^x? Check all that apply.
The function [tex]f(x) = 3(1/3)^x[/tex] represents an exponential decay function. It is described by the following statements: The function [tex]f(x) = 3(1/3)^x[/tex] represents an exponential decay function.
In an exponential decay function, the base of the exponent is between 0 and 1, causing the function to decrease as x increases. In this case, the base is 1/3, which is less than 1, indicating decay. The coefficient 3 represents the initial value or starting point of the function.
As x increases, the function approaches zero, getting arbitrarily close to but never reaching it. Therefore, the function [tex]f(x) = 3(1/3)^x[/tex] is always positive but gradually decreases as x increases. It does not have a horizontal asymptote because it approaches but never reaches zero. It is important to note that the function is defined for all real numbers.
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The complete question is:
Which of the following statements describe the function f(x) = 3(1/3)^x? Check all that apply.
1. The function represents an exponential decay function.
2. The base of the exponent is between 0 and 1.
3. The coefficient 3 represents the initial value of the function.
4. As x increases, the function approaches zero but never reaches it.
5. The function does not have a horizontal asymptote.
6. The function is defined for all real numbers.
what is the value of x in the figure below
Answer:
24
Step-by-step explanation:2x+42= 90
2x=90-42
2x=48
x=24
Step-by-step explanation:
2x°+42°=90°
2x+42°-42°=90°-42°
2x/2=48°/2
x=24°
But Iam not sure I just try
PP 02. 10
2) Mr. Edwin Lazo paid Php 13,600. 00 for a television serMUT UN UN
P16,000. 0. What is the rate of discount?
4. 15%
B. 16%
C. 18%
D. 20%
that regularly sells at Php 1580. 00 is on sale at 30% off. What is the
The rate of discount is 30%. The regular price of the television set is Php 1580, and it is being sold at a discount of 30%.
To find the sale price, we can use the formula:
Sale price = Regular price - (Discount rate × Regular price)
Substituting the given values, we get:
Sale price = 1580 - (0.30 × 1580)
Sale price = 1580 - 474
Sale price = 1106
Therefore, the sale price of the television set is Php 1106. This means that Mr. Edwin Lazo paid Php 13,600.00 for an item that originally cost Php 1580.00 but was on sale at Php 1106.00.
To calculate the rate of discount, we can use the following formula:
Discount rate = (Regular price - Sale price) / Regular price x 100%
Substituting the given values, we get:
Discount rate = (1580 - 1106) / 1580 x 100%
Discount rate = 474 / 1580 x 100%
Discount rate = 0.3 x 100%
Discount rate = 30%
Therefore, the rate of discount is 30%.
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The volume of a cube is 407cm3.
Work out the length of its side rounded to 1 DP.
Given, the volume of a cube is 407cm³.Let's assume that a is the length of a side of the cube. We know that the volume of a cube = a³So,
a³ = 407Take the cube root of both sides to find the value of a.
a = (407)^(1/3)≈ 7.96cm(rounded to 1 decimal place)
Hence, the length of the side of the cube rounded to 1 DP is 7.96 cm (more than 100 words).
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An open cylinder with internal radius r cm has a 2-cm wall and is 9r cm long. Express the volume of material in the wall of the cylinder as a polynomial function in terms of r
The volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]\(r\)[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .
To find the volume of material in the wall of the open cylinder, we need to calculate the difference between the volume of the outer cylinder and the volume of the inner cylinder. The outer cylinder has a radius of [tex]\(r + 2\)[/tex]cm, while the inner cylinder has a radius of [tex]r[/tex] cm. The length of both cylinders is [tex]9r[/tex] cm.
The volume of the outer cylinder can be calculated using the formula: [tex]\(V_{\text{outer}} = \pi \cdot (r + 2)^2 \cdot 9r\) cm^3[/tex].
The volume of the inner cylinder can be calculated using the formula: [tex]\(V_{\text{inner}} = \pi \cdot r^2 \cdot 9r\) cm^3[/tex].
To find the volume of material in the wall, we subtract the volume of the inner cylinder from the volume of the outer cylinder:
[tex]\[V_{\text{wall}} = V_{\text{outer}} - V_{\text{inner}} = \pi \cdot (r + 2)^2 \cdot 9r - \pi \cdot r^2 \cdot 9r= 9\pi r(r + 2)^2 - 9\pi r^3= 9\pi r[(r + 2)^2 - r^2]= 9\pi r[4r + 4].\][/tex]
Simplifying further:
[tex]\[V_{\text{wall}} = 36\pi r^2 + 36\pi r \text{ cm}³ = 36\pi(r^2 + r).\][/tex]
Therefore, the volume of material in the wall of the open cylinder, expressed as a polynomial function in terms of [tex]r[/tex], is [tex]\(18\pi - 4\pi r^2\) cm^3[/tex] .
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Which type of tax describes excise taxes, sales taxes, and tolls?
All three types of taxes fall under the category of indirect taxes because they are not directly based on an individual's income or wealth but rather on the consumption of goods, services,
or use of specific infrastructure.The types of taxes you mentioned, namely excise taxes, sales taxes, and tolls, are all examples of indirect taxes. Indirect taxes are imposed on goods, services, or transactions rather than directly on individuals or entities.
They are typically collected by intermediaries, such as businesses or service providers, who then pass on the tax burden to the consumers.
Excise taxes are levied on specific goods, such as alcohol, tobacco, gasoline, or luxury items. They are often intended to discourage the consumption of these goods or to generate revenue for the government.
Sales taxes are imposed on the sale of goods and services and are usually calculated as a percentage of the purchase price. They are collected by the seller from the buyer at the point of sale.
Tolls, on the other hand, are charges imposed on the use of certain infrastructure, such as roads, bridges, tunnels, or highways.
They are typically collected at toll booths or through electronic systems, and the revenue generated is used for the maintenance and construction of the infrastructure.
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Maria is buying 5 tickets to a play that cost $17 each. She decides to calculate the total cost y doing the following calculation: 5($10)+5($7) = $50+$35= $85 at property is Maria using that allows her to calculate the total cost in this way?
The correct total cost of the 5 tickets is $85.
The calculation that Maria is using to calculate the total cost of the tickets is incorrect. She is multiplying the number of tickets by $10 and $7 separately, instead of multiplying the number of tickets by the cost per ticket.
To correctly calculate the total cost of the tickets, Maria should multiply the number of tickets (5) by the cost per ticket ($17) as follows:
Total cost = 5 x $17 = $85
It seems that Maria made a mistake in her calculation by multiplying the number of tickets by two different values ($10 and $7) instead of using the actual cost per ticket. This mistake leads to an incorrect total cost of $50 + $35 = $85.
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A 14ft ladder leans against the side of a house the angle of elevation of the ladder is 74 how high is the top of the ladder from the ground round to the nearest tenth
The top of the ladder is approximately 44.1 feet from the ground.
To find out how high the top of the ladder is from the ground, we need to use trigonometry, specifically the tangent function since we have the angle of elevation and the length of the adjacent side. Here are the steps to solve the problem:
Step 1: Label the diagram and identify the angle of elevation and the adjacent side.
Label the base of the ladder as the adjacent side (a), the height of the ladder as the opposite side (o), and the length of the ladder as the hypotenuse (h).Identify the angle of elevation as the angle between the adjacent side and the hypotenuse.
In this case, the angle of elevation is 74°.
Step 2: Write out the formula and substitute the given values.Tanθ = o/aTan74° = o/a Solve for o: o = a * tan74°
Step 3: Substitute the value of a and use a calculator to find o.
Substitute the value of a, which is 14 feet, and use a calculator to find o. o = 14 * tan74°o ≈ 44.1 feet (rounded to the nearest tenth)Therefore, the top of the ladder is approximately 44.1 feet from the ground.
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use the distributive property to create true equations 8(3+6) brainly
Here are some true equations that use the distributive property to distribute 8(3+6):
8(3+6) = 8(3) + 8(6) = 24 + 48 = 72
8(3+6) = (83) + (86) = 24 + 48 = 72
8(3+6) = (83) + 68 = 24 + 48 = 72
The distributive property can be used to distribute any number of factors over a sum. In this case, we are distributing the factor 8 over the sum 3+6. We can do this by multiplying each term in the sum by 8 and then adding the products together. This gives us 24 + 48 = 72.
Let f be defined as shown. If the domain is restricted to [9,5}, which statement is true? Click on the correct answer.
The statement "f is not defined for any x-values in the domain [9, 5]" is true. This means that there are no corresponding y-values or outputs for any x-values within this restricted domain. Therefore, The range of f on the domain [9, 5] is approximately equal to [5, 5].
The given question mentions that the domain of function f is restricted to [9, 5]. However, this interval is not valid because the lower bound (9) is greater than the upper bound (5), which contradicts the conventional ordering of intervals. The correct representation of the interval should be [5, 9].
Since the domain [9, 5] is not a valid interval, it means that there are no x-values within this range that can be plugged into function f. As a result, f is not defined for any x-values in the domain [9, 5]. This means that there are no corresponding y-values or outputs for any x-values within this restricted domain.
The range of f on the domain [9, 5] is approximately equal to [5, 5].
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MICE The average length of the head and body of a western harvest mouse is 2.9 inches. The average length of the tail is 2.8 inches. First, estimate the total length of the mouse. Then find the actual total length.
Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.
The given information states that the average length of the head and body of a western harvest mouse is 2.9 inches, while the average length of the tail is 2.8 inches. To estimate the total length of the mouse, we can add these two measurements together:
Estimated total length = Average length of head and body + Average length of tail
Estimated total length = 2.9 inches + 2.8 inches
Estimated total length = 5.7 inches
Therefore, based on the given information, we can estimate that the total length of a western harvest mouse is approximately 5.7 inches.
It's important to note that this estimate represents the average length and may not accurately reflect the actual total length of each individual mouse. There may be variations in the lengths of different mice within the population. Factors such as genetics, age, and environment can influence the actual total length of a mouse. Therefore, the estimate serves as a general approximation and the actual total length of each mouse may differ slightly from the estimate of 5.7 inches.
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Tressa has 57.9 points in a competition. She loses 8.6 points. Write and evaluate an addition expression to determine Tressa's current score.
To write and evaluate an addition expression to determine Tressa's current score, we need to subtract the number of points she loses from her original score. The original score is 57.9 points and she loses 8.6 points.
So, Tressa's current score can be determined by adding the difference (which is -8.6) to her original score. Therefore, the addition expression to determine Tressa's current score can be written as:
57.9 + (-8.6)
To evaluate this expression, we simply need to add the numbers:
57.9 + (-8.6) = 49.3
Therefore, Tressa's current score is 49.3 points.
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Eric is working for an ad firm. He is responsible for storyboarding. Help him specify the different types of audio in the storyboard.
primary audio
secondary audio
background audio
He can make a note of scenes where surrounding noise is required.
>
He can make a note of external microphone to record audio simultaneously while
recording video.
He can make a note of additional music that he wants to add while editing.
Specify primary audio , secondary audio (sound effects/music), and background audio (ambient music) in the storyboard. Note scenes with surrounding noise, use an external microphone for recording, and plan additional music for editing.
In storyboarding for an ad firm, Eric needs to consider three types of audio: primary audio, secondary audio, and background audio. Primary audio refers to the main audio component that drives the narrative or delivers important information in the ad. This can include dialogue, voiceover, or any sound directly related to the main subject. Secondary audio supports the primary audio and adds depth to the storytelling. It can include sound effects, ambient noise, or music that complements the visuals. Background audio provides the overall atmosphere and mood of the ad. It can include ambient music or soundscapes that create the desired emotional tone.
Additionally, Eric should make notes of scenes where surrounding noise is required. This means capturing the environmental sounds that enhance the authenticity and realism of the ad, such as street noise, nature sounds, or crowd reactions. He should also consider using an external microphone to simultaneously record audio while filming the video. This ensures high-quality audio capture and reduces the reliance on the camera's built-in microphone, which may not provide optimal sound recording. Lastly, Eric can make a note of any additional music he intends to add during the editing process. This can involve selecting appropriate background tracks, jingles, or any other musical elements that enhance the overall impact of the ad. By carefully considering these audio aspects during storyboarding, Eric can create a compelling and immersive ad experience for the audience.
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a field project superintenint earns an annual salary of 72800
A field project superintendent earns an annual salary of $72,800. This is a piece of information about the annual salary of a field project superintendent.
A field project superintendent is a person responsible for overseeing and managing construction projects. This position is responsible for ensuring that the construction project is completed on time, within budget, and in accordance with safety and quality standards. This person must have a thorough understanding of construction principles and techniques, as well as the ability to read and interpret blueprints and specifications.
A salary is a fixed amount of compensation paid to an employee for their work. The amount of salary is typically determined by the employee's position, job duties, and level of experience. Salaries are usually paid on a monthly or bi-weekly basis.
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A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The percentile rank of a score of 667 is _________
The percentile rank of a GRE score of 667, based on a population mean of 500 and a standard deviation of 90, is approximately 96.6%.
To calculate the percentile rank of a GRE score of 667, we need to determine how many scores fall below this value in a normal distribution with a mean of 500 and a standard deviation of 90.
First, we calculate the z-score, which represents the number of standard deviations a particular score is from the mean. The z-score can be calculated as (667 - 500) / 90 = 1.8556.
Next, we use a z-table or a statistical calculator to find the area under the normal curve to the left of the z-score. This area represents the percentile rank.
Looking up the z-score in the table or using a calculator, we find that the percentile rank of a score of 667 is approximately 96.6%.
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