The number of hot dogs is 100 while the number of snacks is 75. And it is found by using linear equation.
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the previous sentence, y and x, are referred to as a "linear equation of two variables" at times.
The linear equation to solve the question will be:-
h+s= 175 ------(1)
2.50h + 0.75s = 262.50 -----(2)
From equation (1), s= 175-h -----(3)
Put qeauation (3) into (2) :-
2.50h + 0.75 = 262.50
2.50 + 0.75 (175-h) = 262.50
2.50 + 131.25 - 0.75 = 262.50
Collect like terms :-
2.50-0.75= 262.50-131.25
1.75= 131.25
h= 131.25/1.75
h= 75
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What is the solution to the equation 3x - 2 = 2(2x - 1/2)?
ALGEBRA 1
Answer:
First, you distribute 2(2x-1/2)
2(2x) and 2(-1/2)
Now, you have 3x-2=4x-1
Then, you move 2 to the right side by adding so you can cancel it out.
Then, you move 4x to the left side by doing the same thing with 2
Now, divide both sides by -1
The answer is C, z= -1.
3x-2=2(2x-1/2)
3x-2=4x-1
3x=4x+1
-x=1
-x/-1 = 1/-1
= x=-1
Becky made 10 cups of chocolate mousse for dessert. If she plans to serve each person 1/3 of a cup of chocolate mousse, how many people can she serve? 1/30 people 10 people 3 1/3 people 30 people
The answer is 30 people. Becky can serve 30 people. (Option 4).
To find the number of people Becky can serve, we need to divide the total amount of chocolate mousse she has by the amount each person will be served.
Since Becky has 10 cups of chocolate mousse, we can convert that into the number of 1/3 cup servings by multiplying by 3, which gives us 30 servings.
10 cups ÷ (1/3) cup/serving = 30 servingsTherefore, Becky can serve 30 people with the 10 cups of chocolate mousse she made.
It's important to note that an answer is a whole number, so the options of 1/30 people and 3 1/3 people are not reasonable answers. The correct answer is 30 people.
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Complete Question:
Becky made 10 cups of chocolate mousse for dessert. If she plans to serve each person 1/3 of a cup of chocolate mousse, how many people can she serve?
1/30 people 10 people 3 1/3 people 30 peopleexploraton in math suppose a principal amount of $15,400 is borrowed at a simple interest rate 15% for a period of 13 years. determine the amount of simple interest owed for the use of this loan. round the solution to the nearest cent, if necessary. the amount of simple interest owed is
The amount of simple interest owed for the loan is $30,010.00.
A method for determining the proportion of interest paid on a sum over a predetermined period of time at a predetermined rate is called simple interest. In simple interest, the principal amount remains unchanged. A straightforward and simple method for calculating money interest is simple interest.
To calculate the simple interest, we use the formula:
Simple Interest = P * r * t
where P is the principal amount, r is the interest rate as a decimal, and t is the time period in years.
Substituting the given values, we get:
Simple Interest = $15,400 * 0.15 * 13
= $30,010.00
Therefore, the amount of simple interest owed for the use of the loan is $30,010.00.
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What is the height of the parallelogram?
12 m
A = 186 m²
Answer: 15.5
Step-by-step explanation:
H = A/B
= 186/12
= 15.5
the radius of a sphere decreases at a rate of 3 m / s . find the rate at which the surface area decreases when the radius is 8 m . answer exactly or round to 2 decimal places.
The rate at which the surface area of the sphere is decreasing when the radius is 8 meters and decreasing at a rate of 3 m/s is approximately -192π square meters per second.
Let's start by finding the formula for the surface area of a sphere. The surface area (A) of a sphere with radius (r) is given by the formula:
A = 4πr²
Now, we need to find the rate at which the surface area is changing with respect to time (t) when the radius is 8 meters and the rate of change of radius is 3 m/s.
To find dA/dt, we need to differentiate the formula for surface area with respect to time, using the chain rule:
dA/dt = d/dt (4πr²) = 8πr (dr/dt)
Here, we have used the fact that the derivative of r² with respect to time is 2r (dr/dt) by the chain rule. Now, we can substitute the given values into the formula to find the rate of change of surface area:
r = 8 m (given)
dr/dt = -3 m/s (negative sign because the radius is decreasing)
π ≈ 3.14 (constant)
dA/dt = 8πr (dr/dt)
dA/dt = 8π(8)(-3)
dA/dt = -192π
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What is the value of k?
127.3°
ray fills his car with 45 liters of gasoline every week how many kiloleters of gasoline does his car use in 2 years?
Ray's car will use 4.68 kiloliters of gasoline and travel 39.54 kilometers
Every week, Ray fills his car with 45 liters of gasoline. To calculate the total amount of gasoline used by Ray's car over two years, we must first convert liters to kiloliters. One kiloliter is equal to 1,000 liters, so 45 liters is equal to 0.045 kiloliters. Therefore, in two years, Ray's car will use 0.045 kiloliters x 104 weeks (2 years x 52 weeks per year) = 4.68 kiloliters of gasoline.
To calculate how many kilometers the car will travel with 4.68 kiloliters of gasoline, we need to know the car's fuel efficiency rating. Assuming the car has an average fuel efficiency rating of 8.5 kilometers per liter, we can calculate that the car will travel 8.5 kilometers x 4.68 kiloliters = 39.54 kilometers with 4.68 kiloliters of gasoline.
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A man loses 10 percent by selling his watch for 450 find the cost price of the watch
If a man loses 10 percent by selling his watch for 450 then the cost price of the watch would be 500.
Let's assume the cost price of a watch is 100.
So, after selling at a loss of 10 percent, the selling price of the watch is 90.
By comparing the assumed selling price of the watch with the original selling price, 450/90 = 5.
So, the original selling price is 5 times the assumed selling price.
Thus original cost price should also be 5 times of assumed cost price, so the original cost price × 5 = 100 × 5 = 500.
Hence the original cost price of the watch is 500.
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the amount of jen's monthly phone bill is normally distributed with a population mean of $86 and a population standard deviation of $9. between what two values are 68.26% of her phone bills? $ and $ . (your answers should be integers - no decimal places.)
If the amount of jen's monthly phone bill is normally distributed with a mean of $86 and standard deviation of $9, Between the values of $77 and $95 inclusive, 68.26% of Jen's phone bills are expected to fall.
To find the values between which 68.26% of Jen's phone bills lie, we need to use the properties of the normal distribution and the empirical rule.
The empirical rule states that for a normal distribution, approximately 68% of the data lie within one standard deviation of the mean. Therefore, we can find the values between which 68.26% of Jen's phone bills lie by calculating the range of values that are one standard deviation away from the mean.
Using the given population mean of $86 and population standard deviation of $9, we can calculate one standard deviation as follows:
One standard deviation = population standard deviation = $9
To find the lower and upper bounds for 68.26% of Jen's phone bills, we can subtract and add one standard deviation from the mean, respectively:
Lower bound = population mean - one standard deviation = $86 - $9 = $77
Upper bound = population mean + one standard deviation = $86 + $9 = $95
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Write an equation of a line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8)
Answer:
y=-3x+5
Step-by-step explanation:
A line that is parallel to y=-3x-5 will have the same slope, which is -3.
Using the point-slope form, we can write the equation of the line as:
y - 8 = -3(x + 1)
Simplifying:
y - 8 = -3x - 3
Adding 8 to both sides:
y = -3x + 5
Therefore, the equation of the line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8) is y = -3x + 5.
State the degree of the polynomials
2r^3v + 150r – r^4 v^2
Answer:
11
Step-by-step explanation:
add up the exponents
3+1+1+4+2=11
varsitytutorscom
X^4-3x^2+9x name the polynomial
Answer:
biquadratic polynomial
Step-by-step explanation:
it has degree 4
Please help fast thankyou
Answer:
[tex]y = \frac{2}{7} x - \frac{20}{7} [/tex]
Step-by-step explanation:
[tex] - 2 = \frac{2}{7} (3) + b[/tex]
[tex] - \frac{14}{7} = \frac{6}{7} + b [/tex]
[tex]b = - \frac{20}{7} [/tex]
[tex] y = \frac{2}{7} x - \frac{20}{7} [/tex]
Math help. HEEEEEEEEEEELP.
The expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6.
What is a function f(x)?A function f(x) is a mathematical relationship that assigns a unique output value (or range value) for every input value (or domain value) from a specified set. In other words, a function takes one or more input values and produces a single output value based on a specific rule or set of rules.
According to question:To find g(f(x)), we need to substitute the expression for f(x) into g(x) wherever x appears, since g(x) is being evaluated at the value of f(x). That is, we need to substitute -2x+5 for x in the expression for g(x). This gives:
g(f(x)) = g(-2x+5)
= 3(-2x+5) - 9
= -6x + 15 - 9
= -6x + 6
So, g(f(x)) = -6x + 6.
Therefore, the expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6. Thus, we can express the response as follows:
g(f(x)) = -6x + 6
= [-6]x + [6]
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Helppppppppppppppppp
Debra’s rectangular vegetable garden measures 9 1/3 yards by 12 yards. A bottle of garden fertilizer costs $14.79. If Debra needs to mix 1/8 cup of fertilizer with water for each square yard of her garden, how many cups of fertilizer does she need?
She needs 14 cups of fertiliser.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area = length * width
Find the area of the garden:
Area = 9 1/3 * 12
= 28/3 * 12
= 112 yards²
Find the amount of the fertiliser needed:
1 yards² = 1/8 cup
112 yards² = 1/8 * 112 = 14 cups
She needs 14 cups of fertiliser.
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Identify the asymptotes, domain, and range of each function.
The function f(x) = 5/(x+3), vertical asymptote at x = -3, domain of the function is all real numbers except x = -3, range is all real numbers except 0.
Describe Function?A function is a mathematical object that takes one or more inputs (usually represented as variables) and produces a single output. In other words, a function is a relation between sets of inputs and outputs that associates each input value with exactly one output value.
A function can be represented by an equation or a graph. The most common way to write a function is in the form f(x) = y, where x is the input variable and y is the output variable. The function f maps each value of x to a corresponding value of y.
Functions can be classified based on their properties, such as their domain (set of allowable input values), range (set of output values), and behavior (e.g., increasing, decreasing, constant, etc.). Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions.
The function f(x) = 5/(x+3) has a vertical asymptote at x = -3, since the denominator becomes zero at that point.
The domain of the function is all real numbers except x = -3, since division by zero is undefined.
To find the range, we can consider what happens to the function as x approaches -3 from both sides. As x approaches -3 from the left (i.e., as x gets closer and closer to -3 from values less than -3), the function becomes increasingly negative. As x approaches -3 from the right (i.e., as x gets closer and closer to -3 from values greater than -3), the function becomes increasingly positive. This means that the range of the function is all real numbers except 0.
Therefore, the asymptote is x = -3, the domain is all real numbers except x = -3, and the range is all real numbers except 0.
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What is the standard form of the equation of the circle with the center and a radius of square 2 divided by 4
The standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
To use this formula, we first need to find the values of h, k, and r for the given circle with center and radius of square 2 divided by 4.
We know that the center of the circle is (h, k) = (2/4, -2/4) = (1/2, -1/2).
This means that h = 1/2 and k = -1/2.
The radius of the circle is r = square 2 divided by 4.
We can write this as r² = (square 2 divided by 4)² = 2/16 = 1/8.
Now we can substitute these values into the standard form equation to get:
(x - 1/2)² + (y + 1/2)² = 1/8
So the standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
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Please Help i need the full answer
The value of x in the intersected chord is 72.95 degrees.
How to find the inscribed angle using arc angle?If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
The chords intercepts to form two arc angles 42.9 and 103 degrees. The inscribed angle formed by the intersected chord can be found as follows:
Therefore,
x = 1 / 2 (103 + 42.9)
x = 1 / 2 (145.9)
x = 72.95
Therefore,
x = 72.95 degrees
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the class average on a statistics test is 62 marks with a standard deviation of 12 marks. what minimum mark must a student obtain to be in the top 9% of the class?
Answer:
Step-by-step explanation:
the minimum mark the student should obtain is 32
4) Tom has ran 10 miles of a 75 mile running challenge. If he runs 4 miles each day until he finishes the challenge, write an equation that can be used to find the number of days, d, it will take Tom to finish running the challenge miles.
Step-by-step explanation:
Let's use d to represent the number of days it will take Tom to finish the challenge miles.
Since Tom is currently 10 miles into the challenge and plans to run 4 miles each day until he finishes, the total number of miles he will run is 75 - 10 = 65 miles.
If he runs 4 miles each day, we can use the equation:
total distance = distance per day * number of days
to find the number of days it will take Tom to run 65 miles. Plugging in the known values, we get:
65 = 4d
Simplifying this equation, we can solve for d:
d = 65/4
So, it will take Tom d = 16.25 days to finish the running challenge if he runs 4 miles each day. However, since he cannot run a fraction of a day, we can round up the answer to the nearest whole number of days. Therefore, it will take Tom 17 days to finish the challenge.
The equation that can be used to find the number of days, d, it will take Tom to finish running the challenge miles is:
d = ceil(65/4)
where ceil is the ceiling function, which rounds up the result to the nearest whole number.
Answer:
16 days + 1 mile
Step-by-step explanation:
Can someone please
Help me on this? I’ll give 20 points for this
Answer:
a) 6x10^-6 b) 0.000006 c) I would not be concerned
Step-by-step explanation:
a)
50% is just half and more just means added onto.
Half of 4x10^-6 is 2x10^-6
If you add that onto the original value, you will have:
6x10^-6 (standard form)
b)
0.000006 (ordinary number)
c)
I would not be concerned about the increase in probability of a side effect while using the new medicine. The probability to begin with is extremely low, almost insignificant. While the 50% increase may sound intimidating, it is just a 50% increase on a number that is already very very small. Honestly, it makes almost no difference.
Hi does anyone know how to do problem 2 and 3 on the worksheet?
2. Using percentage, we can find that Melissa needs to save $34500 in order to purchase the house.
3. The project was worth 97 points.
Define percentage?The denominator of a percentage (also known as a ratio or fraction) is always 100.
As a percentage, "%" is read as "percent" or "percentage" in this context.
You may always "divide by 100" this percent symbol to make it into a fraction or decimal equivalent.
Here we can see that Melissa has already $2500 in her savings account.
Total cost of house = $185000
Now for the loan she needs to have 20% of the mortgage as savings.
20% of $185000
20/100 × 185000
= 37000
Now she already has $2500.
So, the amount she need to save is= $37000 - $2500
= $34500
Now, total grade Brooke received = 87.
10 points have been taken off for her mistakes.
Total worth of test = 87+10 =97points.
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I need some help please
Answer:
−18 x + 12
Step-by-step explanation:
multiply using the distributive property
Answer:
-2(9x-6)
-2 divided by 9x = - 18
-2 divided by - 6 = 12 (negative + negative =positive)
= - 18x +12
PLEASE HELP AND PLEASE SHOW ALL STEPS IT WOULD BE VERY MUCH APPRECIATED!!
Answer:
I got to #1 and #3 but I didn't finish in time and I have to leave before I can finish the other ones, my apologies. The solve and steps for 1 and 3 are below. If no one has answered the other two I can probably solve the other two later tonight!
Hope this helps!
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral tris are all 9 feet long, and the height of the equilateral triangle is 7.8 feet. The pyramid's slant heigh feet. What is its surface area?
If a triangular pyramid has a base shaped like an equilateral triangle. its surface area is: 120.41 square feet.
How to find the surface area?To solve this problem, we can use the formula for the surface area of a pyramid:
Surface area = base area + (1/2) x perimeter of base x slant height
First, we need to find the area of the base, which is an equilateral triangle. The formula for the area of an equilateral triangle is:
Area = (square root of 3) / 4 x (side length)^2
Substituting the given values, we get:
Area = (square root of 3) / 4 x 9^2
Area = (square root of 3) x 20.25
Area = 11.06 (rounded to two decimal places)
Next, we need to find the perimeter of the base, which is simply 3 times the side length:
Perimeter = 3 x 9
Perimeter = 27
Finally, we can use the given slant height to find the surface area:
Surface area = 11.06 + (1/2) x 27 x 8.1
Surface area = 11.06 + 109.35
Surface area = 120.41 square feet (rounded to two decimal places)
Therefore, the surface area of the triangular pyramid is approximately 120.41 square feet.
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trough is 10 ft long and its ends have the shape of isosceles triangles that are 3 ft across at the top and have a height of 1 ft. if the trough is being flled with water at a rate of 12 ft 3 ymin, how fast is the water level rising when the water is 6 inches deep?
The water level is rising at a rate of 32 ft/min when the water is 6 inches deep.
How to solve rise of water level?
Let's first draw a diagram to better understand the problem:
/|\
/ | \
/ | \
/ |h \
/ | \
/ | \
/ | \
/ | \
/ | \
/ | \
/_________|
b
where h is the height of the water, b is the width of the trough at water level, and 10 is the length of the trough.
Since the trough is being filled at a rate of 12 ft³/min, the volume of water in the trough is increasing at a rate of 12 ft³/min. Let's use this to find the rate at which the water level is rising.
The volume of water in the trough is given by the formula:
V = (1/2)bh²
where b is the width of the trough at water level, h is the height of the water, and 1/2 is the area of the triangular cross-section of the trough. We want to find the rate at which h is changing when h = 6 inches = 0.5 ft.
Differentiating both sides of the formula with respect to time t, we get:
dV/dt = (1/2)(db/dt)(h^2) + (1/2)(b)(2h)(dh/dt)
where db/dt is the rate at which the width of the trough at water level is changing, and dh/dt is the rate at which the water level is changing (i.e., the rate we want to find).
We know that dV/dt = 12 ft³/min and h = 0.5 ft. We also know that the width of the trough at the water level is 3 ft. To find db/dt, we need to use similar triangles. The triangle formed by the water and the sides of the trough is similar to the isosceles triangle at the end of the trough. Therefore, the ratio of the width of the trough at the water level to the height of the water is constant:
b/h = 3/1
Solving for b, we get:
b = 3h
on diffrentiating
db/dt = 3(dh/dt)
Substituting the values we know into the formula for dV/dt, we get:
12 = (1/2)(3h)(h²) + (1/2)(3h)(2h)(dh/dt)
12 = (3/2)h³+ 3h²(dh/dt)
4 = h²(dh/dt)
Solving for dh/dt, we get:
Therefore, the water level is rising at a rate of 32 ft/min when the water is 6 inches deep.
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Physics graduate student Laura Van Ertia has conducted a complete randomized design with a single factor, hoping to solve the mystery of the unified theory and complete her dissertation. The results of this experiment are summarized in the following ANOVA display:What is the sum of squares for the factor?
Remember, accurate interpretation of the results is essential for the success of Laura's dissertation.
The sum of squares for the factor in Laura Van Ertia's experiment can be found in the ANOVA display. ANOVA stands for Analysis of Variance, and it is a statistical method used to compare the means of two or more groups. The sum of squares is a measure of the variation within the data, and it helps to determine whether the differences between groups are statistically significant.
In the given question, you have not provided the actual ANOVA display, which is necessary to determine the sum of squares for the factor. The ANOVA table typically consists of columns for sources of variation (such as between groups and within groups), degrees of freedom, sum of squares, mean squares, F-ratio, and p-value. The sum of squares for the factor can be found in the 'sum of squares' column corresponding to the between-group variation row.
Once you have the ANOVA display, locate the sum of squares for the factor and use it in your analysis to understand the results of the experiment and its implications on the unified theory.
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x(z ÷ 3)^2 where x = 4 and z = 9 calculate
Answer: 36
Step-by-step explanation:
4(9/3)(2) = 36
Answer:
x(z ÷ 3)² = 36
Step-by-step explanation:
Given expression,
→ x(z ÷ 3)²
Now we have to use,
→ x = 4
→ z = 9
Let's simplify the expression,
→ x(z ÷ 3)²
→ 4(9 ÷ 3)²
→ 4 × (3)²
→ 4 × 9
→ 36 => {answer}
Therefore, the answer is 36.
(1/32)^x=8^3-x solve for x
We can rewrite the right side of the equation as a power of 2 since 8 = 2^3:
(1/32)^x = (2^3)^3-x
Simplifying the right side:
(1/32)^x = 2^(9-3x)
We can write both sides using a common base, say 2:
2^(-5x) = 2^(9-3x)
Now we equate the exponents and solve for x:
-5x = 9 - 3x
-2x = 9
x = -4.5
Therefore, the solution to the equation is x = -4.5.