Answer:
x-int: (2, 0)
y-int: (0,8)
(8-0)/(0-2)= 8/-2= -4
y - 0 = -4(x - 2)
y = -4x + 8
Step-by-step explanation:
Forty-seven percent of fish in a river are catfish. Imagine scooping out a simple random sample of 25 fish from the river and observing the sample proportion of catfish. What is the standard deviation of the sampling distribution? Determine whether the 10% condition is met.
The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.0998. The 10% condition is not met because there are less than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
The standard deviation is 0.9002. The 10% condition is not met because there are less than 250 catfish in the river.
We are unable to determine the standard deviation because we do not know the sample mean. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Answer:
Therefore the correct option is a.) The standard deviation is 0.0998. The 10% condition is met because it is very likely there are more than 250 catfish in the river.
Step-by-step explanation:
i) Let p = 0.47
ii) therefore q = 1 - 0.47 = 0.53
iii) sample size, n =25
iii) standard deviation = [tex]\sqrt{\frac{p \times q}{n} } = \sqrt{\frac{0.47 \times 0.53}{25} } = 0.0998[/tex]
Therefore the correct option is
a.) The standard deviation is 0.0998. The 10% condition is met because it
is very likely there are more than 250 catfish in the river.
The standard deviation of the sampling distribution of the sample proportion is 0.0998. To determine whether the 10% condition is met, the total population of catfish should be at least 10 times the sample size.
Explanation:The question asks about determining the standard deviation of the sampling distribution of the proportion of catfish in a river and if the 10% condition is met for the sampling distribution to be approximately normal. First, to calculate the standard deviation of the sampling distribution of the sample proportion (p-hat), we use the formula √[(p(1-p))/n], where p is the population proportion and n is the sample size. In this case, p = 0.47, so 1 - p = 0.53, and n = 25. The standard deviation is then √[(0.47*0.53)/25], which is approximately 0.0998.
Next, the 10% condition checks whether we can consider the population large enough that the sample size doesn't affect the population proportion notably when taking without replacement. This condition states that the sample size, n, should be no more than 10% of the population. If there are indeed more than 250 fish in the river (10 times the sample size), we can be confident that the 10% condition is met. If not, the condition is not met.
Therefore, the correct response would state the standard deviation and appropriately evaluate whether the 10% condition is met based on the estimated number of catfish in the river.
A gym charges $25 per month plus $4 extra to swim in the pool for an hour. If a member only has $45 to spend each month, at most how many hours can the member swim? Write an equation and demonstrate this on a number line.
Graph: y-3=1/2(x+2)
Where would i graph this please help me just tell me the points dont go over the top with explanation
The plotted line on the graph represents all the points (x, y) that satisfy the equation [tex]\( y - 3 = \frac{1}{2}(x + 2) \)[/tex].
The graph of the equation [tex]\( y - 3 = \frac{1}{2}(x + 2) \)[/tex] has been plotted. Here are the steps to plot this graph:
1. Rearrange the equation: Convert the given equation into slope-intercept form, [tex]\( y = mx + c \)[/tex], which makes it easier to graph.
The given equation is [tex]\( y - 3 = \frac{1}{2}(x + 2) \)[/tex]. By rearranging, you get [tex]\( y = \frac{1}{2}x + 1 + 3 \)[/tex] which simplifies to [tex]\( y = \frac{1}{2}x + 4 \)[/tex].2. Calculate the y-intercept: This is the point where the line crosses the y-axis, which occurs when [tex]\( x = 0 \)[/tex]. Substituting [tex]\( x = 0 \)[/tex] into the equation gives [tex]\( y = 4 \)[/tex]. So, the y-intercept is (0, 4).
3. Calculate the slope: The slope is [tex]\( \frac{1}{2} \)[/tex] which means that for every 2 units the graph moves horizontally to the right, it moves 1 unit up.
4. Plot the y-intercept: Start at the y-intercept (0, 4) on the graph.
5. Use the slope to find another point: From the y-intercept, move right 2 units and up 1 unit to find another point on the line. You could also move left 2 units and down 1 unit for another point.
6. Draw the line: Connect the points with a straight line to complete the graph.
what are the two values of x that are roots of this equation x^2+3x-6=0
Answer:
x = - 3 - √33 / 2
x = + 3 + √33 /2
or
x=1.37228132...
x=−4.37228132...
Step-by-step explanation:
The two values of x that are roots of the equation x^2+3x-6=0 are approximately x ≈ -4.16 and x ≈ 1.16.
Explanation:To find the two values of x that are roots of the equation x^2+3x-6=0, we can use the quadratic formula. The formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 3, and c = -6. Plugging in these values, we get:
x = (-3 ± √(3^2 - 4(1)(-6))) / 2(1)
Simplifying further:
x = (-3 ± √(9 + 24)) / 2
x = (-3 ± √33) / 2
So the two values of x that are roots of the equation are approximately x ≈ -4.16 and x ≈ 1.16.
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In the problem 4x + 10 list a constant.
Answer:
10
Step-by-step explanation:
Constant term consists of natural no.s or numerals
So here the constant is 10
Answer:
In the problem 4x + 10 , 10 is the constant
Step-by-step explanation:
In the problem 4x + 10 , 10 is the constant
As we know
In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
Examples:
In "x + 5 = 9", 5 and 9 are constants.
similarly
In x+ a= b , a and b are constants
so from definition of constant in algebra it is clear that
in
The problem 4x + 10 , 10 is the constant
1) In the diagram, l || m. If the measure of angle 3 is 120 find the measure of the following angles
a) angle 4
b) angle 6
c) angle 8
Answer:
a) 60° , b) 120° and c) 60°
Step-by-step explanation:
See the diagram attached to this question.
a) Here, ∠ 4 and ∠ 3 are supplementary angles.
So, ∠ 4 + ∠ 3 = 180° {Here, ∠ 3 is given to be 120°}
⇒ ∠ 4 = 180° - ∠ 3 = 180° - 120° = 60° (Answer)
b) Now, ∠ 3 and ∠ 6 are alternate angles and hence, ∠ 3 = ∠ 6 = 120° (Answer)
c) Here, ∠ 6 and ∠ 8 are supplementary angles.
So, ∠ 6 + ∠ 8 = 180°
⇒ ∠ 8 = 180° - ∠ 6 = 180° - 120° = 60° (Answer)
Camacho is buying a monster truck. The price of the truck is xxx dollars, and he also has to pay a 13\%13%13, percent monster truck tax.
Which of the following expressions could represent how much Camacho pays in total for the truck?
Answer:
Camacho pays in total for the monster truck = $x + $0.13x = $1.13x
Step-by-step explanation:
i.) The price of truck is $x
ii.) Monstor truck tax = 13% of price of truck = [tex]\frac{13}{100}\times $x[/tex] = $0.13x
iii) Camacho pays in total for the monster truck = $x + $0.13x = $1.13x
Options A and D correctly represent how much Camacho pays in total for the truck:
A. (1 + 0.13)x
D. 1.13x
The total amount Camacho pays for the monster truck includes the price of the truck plus the tax, which is 13% of the price of the truck. Therefore, the total amount can be represented by the expression:
[tex]\[ \text{Total amount} = \text{Price of the truck} + \text{Tax amount} \][/tex]
Given that the price of the truck is x dollars and the tax is 13\% of the price, we can represent the tax amount as 0.13x .
So, the total amount Camacho pays is:
[tex]\[ \text{Total amount} = x + 0.13x \][/tex]
[tex]\[ \text{Total amount} = 1.13x \][/tex]
Therefore, options A and D correctly represent how much Camacho pays in total for the truck:
A. (1 + 0.13)x
D. 1.13x
The complete Question is given below:
Camacho is buying a monster truck. The price of the truck is x dollars, and he also has to pay a 13% monster truck tax. Which of the following expressions could represent how much Camacho pays in total for the truck? Choose 2 answers:
A. (1+0.13)x
B. 13x/100
C. 13x
D. 1.13x
E .13x+x
How much cashews at $1.58 per pound must be mixed with walnuts that cost 78 cents per pound to make a mixture of 40 pounds of nuts that cost $1.50 per pound?
Answer:
Cashew= 36 pounds
Walnut= 4 pounds
Step-by-step explanation:
Given: Cost of Cashew= $1.58 per pound
Cost of walnut= $0.78 per pound
Total weight of mixture= 40 Pound
Cost of mixture= $1.50 per pound.
Lets assume the amount of cashew added in the mixture be "x".
∴ Amount of Walnut in the mixture will be [tex](40-x)[/tex]
Now, forming an equation to total cost and weight of mixture.
⇒ [tex]1.58\times x+0.78 \times (40-x)= 40\times 1.50[/tex]
Using distributive property of multiplication
⇒ [tex]1.58x+31.2-0.78x= 60[/tex]
⇒[tex]0.8x+31.2= 60[/tex]
Subtracting both side by 31.2
⇒[tex]0.8x= 60-31.2[/tex]
⇒[tex]0.8x= 28.8[/tex]
Dividing both side by 0.8
⇒[tex]x= \frac{28.8}{0.8}[/tex]
∴ [tex]x= 36\ pounds[/tex]
Hence, Amount of cashew added in the mixture of nuts is 36 pounds.
Next finding the amount of walnut added in the mixture.
subtituting the value of x
Amount of walnut in the mixture= [tex](40-x)[/tex]
⇒ Amount of walnut in the mixture= [tex](40-36)= 4\ pounds[/tex]
Hence, 4 pounds of walnut added in the mixture.
Final answer:
To make a 40-pound mixture of nuts that costs $1.50 per pound, mix 36 pounds of cashews, which cost $1.58 per pound, with walnuts costing $0.78 per pound.
Explanation:
Let's approach this mixture problem using the concept of weighted averages. We know we want to make a 40-pound mixture of cashews and walnuts that costs $1.50 per pound.
The cashews cost $1.58 per pound and the walnuts cost $0.78 per pound. To find out how many pounds of cashews to mix with walnuts, we can set up the equation:
Let x be the amount of cashews needed.
Since the total weight of the mixture is 40 pounds, the amount of walnuts needed would be 40 - x pounds.
Using the equation for the total cost of the mixture: 1.58x + 0.78(40 - x) = 1.50(40),
we solve for x:
1.58x + 31.2 - 0.78x = 600.8x = 28.8x = 36Therefore, to obtain a 40-pound mixture costing $1.50 per pound, a person should mix 36 pounds of cashews with walnuts.
On Friday a local hamburger shop sold a combined total of 304 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
76 hamburgers
Step-by-step explanation:
3x + x = 304
4x = 304
what times 10 equals 0.3
To find out what number times 10 equals 0.3, you divide 0.3 by 10. The answer is 0.03.
Explanation:The question you're asking is essentially what number, when multiplied by 10, equals 0.3. This is a basic division problem in mathematics, because when you want to find out what number multiplied by another number gives a certain result, you divide the result by one of the numbers.
In this case, you would divide 0.3 by 10. So, the solution to this problem is: 0.3 / 10 = 0.03.
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The number that times 10 equals 0.3 is 0.03. This exercise relates to understanding decimal places and exponents, where for instance, 10⁻³ represents 0.001 and signifies that the decimal point is shifted three places to the left.
To find what number times 10 equals 0.3, we need to solve the following equation:
x × 10 = 0.3
To find x, we divide both sides of the equation by 10:
x = 0.3 / 10
x = 0.03
Therefore, 0.03 times 10 equals 0.3.
Use the drop-down menus to complete the statement about the inequality m ≥ 2.
Answer:
The inequality m ≥ 2 has infinity many solutions because 2 and any number to the right of 2 on the number line can be substituted for m to make this inequality true.
count backwards by hundreds from 1,000.
Answer:
1,000 900 800 700 600 500 400 300 200 100
Step-by-step explanation:
Simplify the radical 147
Answer and Explanation: The square root of 147 is approximately 12.12436 or 7√3 in radical form. To begin, examine 147's factors. These are: 1, 3, 7, 21, 49, 147.
Hope this helped
Answer:
12.12436 or 7√3
Step-by-step explanation:
solve this system of equations by using substitution
3x + 5y = 23
y= x + 3
Answer:
x=1
y=4
(1,4)
Step-by-step explanation:
TO SOLVE FOR X:
1. Substitute y=x+3 into the equation. This should look like this:
3x+5(x+3)=23
2. Use the distributive property.
3x+5x+15=23
3. Simplify:
8x+15=23
4. Subtract 15 from both sides. It should now lool like this:
8x=8
5. Divide both sides by 8.
x=1
TO SOLVE FOR Y:
1. Take x and substitute into original statement:
3(1)+5y=23
2. Simplify:
3+5y=23
3. Subtract 3 from both sides:
5y=20
4: Simplify:
y=4
CHECK ANSWER:
y=x+3
1. Substitute your answers
4=1+3
2. Simplify
4=4
3. Check for Truth. Is 4=4?
Yes. So your final answer is:
x=1
y=4
(1,4)
Write a numerical expression representing the following statement:
"four times the sum of sixty-seven plus forty"
Answer:
47 + 40 x 4
Step-by-step explanation:
sum is adding 2 numbers together and you would then multiply 4 after adding :)
[Question Image Attached] If you are given the graph of g (x) = log 2 x, how could you graph f (x) = log 2 x + 5?
Answer:
Translate each point of g(x) 5 units up.
Step-by-step explanation:
The given the graph of the parent function
[tex]g(x) = log_{2}(x) [/tex]
We want to use this graph to draw the graph of
[tex]f(x) = log_{2}(x) + 5[/tex]
We can observe that:
[tex]f(x) = g(x) + 5[/tex]
This means the graph of the parent function, g(x) must be shifted up 5 units.
Therefore the correct answer is A.
A study indicated that the citizens of Newport wasted 38,080 gallons of water last year. This year they wasted 20% less. How many gallons did the citizens wasted this year
A company is expanding its building area from 11,000 square feet to 14,740 square feet. What is the percentage increase of the area
of the building space?
A. 66%
B. 37.4%
C. 3.4%
D. 34%
Option D
The percentage increase of the area of the building space is 34 %
Solution:
A company is expanding its building area from 11,000 square feet to 14,740 square feet
To find: Percentage Increase
The percent increase is given by formula:
[tex]\text{Percent increase } = \frac{\text{Final value - Initial value}}{\text{Initial value}} \times 100[/tex]
From given,
Initial value = 11000
Final value = 14740
Substituting we get,
[tex]Percent\ Increase = \frac{14740-11000}{11000} \times 100\\\\Percent\ Increase = \frac{3740}{110}\\\\Percent\ Increase = 34[/tex]
Thus percentage increase of the area of the building space is 34 %
Charlotte uses a 50% off coupon when she buys a dress the original price of the dress is $45 how much money does Charlotte save by using the coupon
Answer: $22.50
Step-by-step explanation:
Since the price is 50% off, you need to find half of 45. 45/2 is 22.5, so she saves $22.50
-3 x [75/(9 - 4)^2]^2 simplify
Answer:
[tex]-27x[/tex]
Step-by-step explanation:
Given Equation:
[tex]-3 x [75/(9 - 4)^2]^2[/tex]
On simplifying the equation:
[tex]=-3 x [75/(9 - 4)^2]^2\\=-3 x [75/(5)^2]^2\\=-3 x [75/25]^2\\=-3 x [3]^2\\=-3x*9\\=-27x[/tex]
The value of 'x' can be find by equating the simplified value to some certain value according to the equation.
Leah has The flowers shown she wants to put them in 4 vases with the same number in each case how many flowers does she need to put in each case
The number of flowers she need to put in each case is [tex]\frac{x}{4}[/tex]
What is flowers she need to put in each case?The area of mathematics known as algebra is responsible for helping to express circumstances or problems as mathematical expressions. Divide the total number of flowers by the total number of vases to find the solution. We can still demonstrate how to solve the problem even if we do not have all the quantities.
x = total number of flowers.
There are 4 vases.
Therefore, the number of flowers in each vase will be [tex]\frac{x}{4}[/tex]
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please help :(( i gotta hurryy >
The polynomial that represents the area of the given rectangle is [tex]32x^2+16x+2.[/tex]
Step-by-step explanation:
We are given with a rectangle which has the length and breadth.
Also the length and breadth is given in the form of polynomial.
The length of the rectangle = 2(4x+1).
which can also be written as 8x+2.
The breadth of the rectangle= 4x+1
Area of the rectangle A= length × breadth.
⇒A=(8x+2)×(4x+1).
=[tex]32x^2+8x+8x+2.[/tex].
=[tex]32x^2+16x+2.[/tex]
Thus the area of the given rectangle is [tex]32x^2+16x+2.[/tex]
Perry Angelo is planning to open a restaurant. He has the resources to produce and sell either hamburgers or pizzas. So he does some research
and finds that the new location has a good demand for pizza. He hires cooks, wait staff, and an accounts person for his new pizzeria. He also
arranges for materials such as pizza ingredients and pizza boxes.
Determine three factors affecting Perry's cost of making pizza. Write down the name of the factors and their instances in this scenario in the table.
Answer:
Factors Affecting Cost Factors Affecting Cost
opportunity cost: the opportunity to produce and sell
hamburgers
cost of materials: cost of pizza ingredients and pizza boxes
sunk cost: money spent on researching the best option
fixed cost: money for paying employees
marginal cost:the cost of baking one more pizza
Step-by-step explanation:
Perry Angelo's cost of making pizza is affected by the cost of ingredients, labor costs, and capital costs like the pizza oven and shop rent. These costs, along with a desired profit margin, influence the selling price.
Explanation:The cost of producing pizza or any output involves various factors. In the scenario described for Perry Angelo's pizzeria, three significant factors affecting the cost of making pizza include:
Cost of Ingredients: This includes items like dough, sauce, cheese, and pepperoni, which are essential for making pizzas.Labor Costs: The wages paid to the cooks, wait staff, and the accounts person Perry Angelo hires.Capital Costs: Investments made in the pizza oven and other equipment necessary for the production of pizzas, as well as ongoing expenses like shop rent.These elements contribute to the total production cost, on top of which Perry will need to add his desired profit margin to determine the selling price for the pizzas.
Question 16(Multiple Choice Worth 1 points)
(06.02 LC)
Which statement best describes the expression 4y ÷ 9?
9 divided by 4 times y
9 times y divided by 4
4 times y divided by 9
4 divided by 9 times y
Answer:
4 times y divided by 9
Step-by-step explanation:
4y means 4×y which is 4 times y that is divided by 9
A bag contains 15 navy and 26 violet marbles. A marble is drawn at random.
What is the theoretical probability of drawing a violet marble?
Find the lengths of AB,BC,PQ,and QR. Which segments have equal lengths?
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 69 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 65 miles per hour and 73 miles per hour. (Assume the data set has a bell-shaped distribution)
This is the answer, I hope it will be help
The percent of vehicles whose speeds are between 65 miles/hour and 73 miles/hour will be 68 %.
It is given that mean speed of sample of vehicles (μ) is 69 miles/hour and standard deviation is 4 miles/hour.
We have to find out the percent of vehicles whose speeds are between 65 miles/hour and 73 miles/hour using the empirical rule.
What is the empirical rule if distribution lies within one standard deviation from the mean ?
The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean.
As per the question , we have ;
Mean speed of sample of vehicles (μ) = 69 miles/hour
Standard deviation = 4 miles/hour
To find the % of vehicles , let's check where the distribution lies ;
So ;
μ - 4 ;
= 69 - 4
= 65 miles / hour
μ + 4 ;
= 69 + 4
= 73 miles / hour
Since ; it lies between μ - 4 and μ + 4 , so by using the empirical rule we get that it lies within one standard deviation.
Hence ; by the empirical rule ;
% of vehicles between speed 65 miles/ hour and 73 miles/hour = 68 %
Thus , the percent of vehicles whose speeds are between 65 miles/ hour and 73 miles/hour will be 68 %.
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Help with two Math problems.
1: A bag of dog food weighs 20lb. 15% of the weight is oats.
a) Set up an equation OR proportion to find the weight of the oats in the dog food.
b) What is the weight of the oats in the dog food? Show your work.
2: Some students were asked what kind of animals they have at home. The results are in the image:
(a) List the animals in order of popularity from most popular to least popular.
(b) I estimated that 250 students were interviewed. Based on my estimate, how many students have an "other" pet? Show your work.
Answer:
1. a. o = 3b
b. o = 3 pounds
2. a. Most popular animals:
A. Dogs - 67%
B. Cats - 20%
C. Other - 8%
D. None - 4%
E. Horses - 1%
b. 20 students
Step-by-step explanation:
1. a. The equation is:
o = 0.15 *20b
o = 3b
where, o = weight of oats in pounds and b = number of dog food bags
b. Let's find out the weight of the oats in one dog food bag, using our equation:
o = 0.15 *20b
o = 0.15 *20 * 1
o = 3 pounds
2. a. Most popular animals:
A. Dogs - 67%
B. Cats - 20%
C. Other - 8%
D. None - 4%
E. Horses - 1%
b. If 250 students were interviewed, the 8% who answered "other" are:
8% of 250 = 0.08 * 250 = 20 students
Emmanuel sold 16 dozen eggs last month. How many eggs did he sell in all?
Answer:
Emmanuel would have sold 192 eggs total
Step-by-step explanation:
one dozen is 12 eggs
16 dozen would be 12 x 16 = 192
Emmanuel would have sold 192 eggs total
Emmanuel sold 16 dozen eggs, and since one dozen equals 12 items, the total number of eggs sold is 192 eggs.
Explanation:The student asked how many eggs Emmanuel sold last month if he sold 16 dozen. To answer this question, we need to understand that one dozen represents 12 items. Therefore, if Emmanuel sold 16 dozens of eggs, we use multiplication to find the total.
First, identify the number of items in a dozen: 12 eggs.Next, multiply the number of dozens sold by the number of items in one dozen: 16 dozens x 12 eggs/dozen = 192 eggs.So, Emmanuel sold a total of 192 eggs last month.
Answering the additional example questions for clarification:
For g., the number is two and the unit is dozen eggs, because 'two' specifies the quantity of dozens, not individual eggs.For h., the unit is dozen eggs because that combines the measurement unit 'dozen' with what's being measured, in this case, eggs.For i., the blank should be filled with the conversion: 1 km = 1000 metersTo identify the number and unit in each quantity provided:
a. The number is one, and the unit is a dozen eggs.b. The number is 2.54, and the unit is centimeters.c. 'A box' is the number, and 'pencils' is the unit.d. The number is 88, and the unit is meters per second.How to write a point slope form of the equation of a line with a slope of -4 and passes through the point (1,6)?
Answer:
y-6=-4(x-1)
Step-by-step explanation:
y-y1=m(x-x1)
y-6=-4(x-1)