Answer:
35 small pies
Step-by-step explanation:
Framing system of linear equations and solving:Let the number of large pies be 'l' and
The number of small pies be 's'.
Total pies sold = 45
⇒ l + s = 45 ------------(I)
l = 45 - s -------(II)
Cost of 45 pies = $120
Cost of 1 large pie = $5
Cost of 'l' large pies = 5*l = 5l
Cost of 1 small pie = $2
Cost of 's' small pie = 2*s = 2s
5l + 2s = 120 --------------(III)
Solving : substitution method
Substitute l = 45 -s in equation (III)
5*(45 - s) + 2s = 120
5*45 - 5*s + 2s = 120
225 - 5s + 2s = 120 {Combine like terms}
225 - 3s = 120
-3s = 120 - 225 {Subtract 225 from both sides}
-3s = -105
s = -105 ÷ (-3) {Divide both sides by (-3)}
s = 35
Substitute s = 35 in equation (II),
l = 45 - s
= 45 - 35
l = 10
[tex]\sf \boxed{\text{\bf 35 small pies were sold}}[/tex]
This table represents function f. If function g is a quadratic function that contains the points and , which statement is true over the interval ? A. The average rates of change of f and g cannot be determined from the given information. B. The average rate of change of f is less than the average rate of change of g. C. The average rate of change of f is the same as the average rate of change of g. D. The average rate of change of f is more than the average rate of change of g.
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), the statement which is true over the interval [-3, 0] is: B. The average rate of change of f is less than the average rate of change of g.
What is an average rate of change?An average rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes (decreases or increases) with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of function f over the interval [-3, 0]:
a = -3; f(a) = -4.5
b = 0; f(b) = 0
Substituting the given parameters into the formula, we have;
Average rate of change = (0 - (-4.5))/(0 - (-3))
Average rate of change = 4.5/3
Average rate of change = 1.5.
Also, we would determine the average rate of change of function g over the interval [-3, 0]:
a = -3; f(a) = 5
b = 0; f(b) = 14
Substituting the given parameters into the formula, we have;
Average rate of change = (14 - 5)/(0 - (-3))
Average rate of change = 9/3
Average rate of change = 3.
In conclusion, the average rate of change of function f is less than the average rate of change of function g.
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Answer:
The average rate of change of f is less than the average rate of change of g.
Step-by-step explanation:
Plato/Edmentum
What is the percentage efficiency of a motor that does 60J of work from 240J of electrical energy?
Answer:
25% is the correct answer
7. Health experts recommend the average female older than 50 years of age to
consume about 1,800 calories per day.
• Mrs. Keith has already consumed 950 calories today.
She plans to consume the same number of calories per hour for
the next 5 hours.
.
Which inequality represents d, the number of calories Mrs. Keith could eat each hour
for the next 5 hours without exceeding her recommended daily caloric intake?
The slope of the graph
Answer:
5 x + 4 y = 4 b
Step-by-step explanation:
You haven't specified what form you need. Here is the Standard form, but you can also calculate the Slope intercept form points and the Point-Slope form.
Find the equation of the line in standard form with the properties:
slope: m = -5/4
At least two parameters must be provided to determine a line equation:
Since the line is incompletely determined, compute the equation assuming an arbitrary y-intercept b
Substitute the slope m = -5/4 into the slope-intercept equation y = m x + b:
y = -(5 x)/4 + b
Add (5 x)/4 to both sides:
(5 x)/4 + y = b
Multiply both sides by 4:
4 ((5 x)/4 + y) = 4 b
Distribute: 4 ((5 x)/4 + y) = 5 x + 4 y:
Answer: 5 x + 4 y = 4 b
a janitor had 3/5 of a spray bottle of a cleaning solution . he used 1/9 of the soloution in a day. how much of the bottle did he use?
The Janitor used 8/15 of the bottle
How to calculate the amount of the solution of the bottle used ?
The Janitor has 3/5 of a spray bottle solution
He uses 1/9 of the solution in a day
The amount of solution used can be calculated as follows
3/5 × 1/9
= 3/45
= 1/15
The initial amount in the bottle is
3/5 - 1/15
= 8/15
Hence the amount of solution he has used is 8/15
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If a first integer is represented by the variable x, then which of the following would be the next four consecutive odd integers?
Choose the correct answer below.
A. x+1, x+2, x+3, x+4
B. x+2, x+4, x+6, x+8
Points: 0 of 1
C. x, x+2, x+4, x+6
OD. x+1, x+3, x+ 5, x+7
the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.
We are given that:
The first integer is represented by the variable x.
We need to find the next four consecutive odd integers.
We know that the difference between the two consecutive odd integers will always be 2.
So, this means, we can always get the next odd integers by adding 2 to the previous one.
So, we get that:
x + 2
x + 2 + 2 = x + 4
x + 4 + 2 = x + 6
x + 6 + 2 = x + 8
Therefore, we get that, the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.
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Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip.
How much did they get altogether?
Answer:
Let Pip get = x
Fiona gets = x + 35
Ratio = 6:1
x+35/x = 6
x + 35 = 6x
5x = 35
x = 7
Total money = x + x + 35 = 14+ 35 = £49
Answer:
£49
Step-by-step explanation:
Fiona gets 35 more than Pip so 6-1 =5 and 5 portions = 35
so 1 portion = 7
7x6 = 42
7x1 =7
7+42 = 49
so they got £49
hope this works :)
someone pls help me w this. I rlly need this!! thank uu!
"write the equation of a line that is parallel to y=2x-3 and passes through the point (1, 6)"
Leila wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are feet. Suppose each can of paint will cover square feet. How many cans will she need to paint the ceiling?
Answer: Find the square roots and the multiply that by 4
Step-by-step explanation:
hope this helped
Find m
A
2x
C
(3x - 10)
D
E
B
Answer:
∠ABC = 40
∠CBC = 50
Step-by-step explanation:
∠ABC + ∠CBD = 90
2x + (3x - 10) = 90
2x + 3x - 10 = 90
5x = 100
x = 20
∠ABC = 2x = 2(20) = 40
∠CBC = 3x - 10 = 3(20) - 10 = 50
f(x) = -2x + 10, If f(x)= 40, what is the value of x? (find the input)
Answer:
-15
Step-by-step explanation:
set it up
f(40)=-2x+10
40=-2x+10
subtract ten
30=-2x
divide by -2 to isolate the x
-15=x
Answer:
f(x) = -2x + 10
If f(x)= 40
By using equation,
or, 40=-2x+10
or, 40-10=-2x
or, 30=-2x
or, 30/-2=x
Therefore x=-15
The graph below shows the distance a helicopter traveled over time. Find the rate of change from 1 hour to 2 hours.
The rate of change from 1 hour to 2 hours will be 125 miles per hour. Option C is correct.
What is linear equation?
A relationship between two or more parameters that, shown on a graph, produces a linear model. The degree of the variable will be one.
Given that;
Two points on the graph are (1, 125) and (2, 250).
Now, The slope of the line is calculated as;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Hence, Slope of the line passes through the points (1, 125) and (2, 250).
m = (250 - 125) / (2 - 1)
m = 125
So, The rate of change from 1 hour to 2 hours will be 125 miles per hour.
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does the ratio 2/5 to 1/3 has a unit rate of 2/15
The statement that the ratio 2/5 to 1/3 has a unit rate of 2/15 is; True
How to find the unit rate?
A unit rate is defined as a rate for one of something. This can be written as a ratio with a denominator of one.
For example, if you ran 50 meters in 10 seconds, you ran an average 5 meters in 1 second. Both of the ratios, 50 meters in 10 seconds and 5 meters in 1 second, are rates, but the 5 meters in 1 second is a unit rate.
We are given the ratio 2/5 to 1/3. Now, this can be expressed as;
(2/5)/(1/3) = 2/5 * 1/3 = 2/15
Thus, this corresponds with the given unit rate of 2/15.
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perform the indicated operation and simplify the result leave yuour answer in factored form 4x/x2 - 1
The simplified result is :
[tex]4x/x^{2}[/tex] - 1
= 4/x -1
4-x / x.
Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.
An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.
In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression often means applying them.
To know more about "Factored Form"
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Chelsea and nine of her friends went out to eat. They decided to split the bill evenly. Each person paid $21.00. What equation would depict this scenario
Answer:
21(10)
Step-by-step explanation:
youll have to do 21 times 10
Answer:
[tex]\frac{210.00}{10}[/tex] = x
Step-by-step explanation:
[tex]\frac{210.00}{10}[/tex] = x
Let x is the number that each person needs to pay.
Hayley wants to be a marine biologist when she grows up. Her entire room is ocean-themed, so she is painting her bed frame blue to match. She estimates that she will need 800 milliliters of paint, but the hardware store only sells paint in liters. If Hayley buys 1 liter of paint, how many milliliters will she have left?
Answer:
Hayley will have 200 milliliters of paint left.
Step-by-step explanation:
1 liter=1000 milliliter
1000-800=200
Answer:
305
Step-by-step explanation:
There are 1,000 milliliters in 1 liter.solveYou need to find how many milliliters of blue paint Annie has left. But first, you need to know how many milliliters she started with.There are 1,000 milliliters in a liter, so multiply 0.5 liters by 1,000.0.5×1,000=500Annie started with 500 milliliters of blue paint.Now, add to find how much blue paint Annie used for her beach painting. She used 75 milliliters of blue paint for the sky and 120 milliliters for the ocean.75+120=195Annie used 195 milliliters of blue paint in all.Now, find how much blue paint Annie has left. She started with 500 milliliters. Subtract the 195 milliliters she used.500–195=305Annie has 305 milliliters of blue paint left.
A piece of machinery depreciates at a fixed rate of 12% per year for 7 years. If the machinery is valued at $100,000 after 7 years, how much would the machinery have initially cost rounded to the nearest dollar?
a.
$113,636
d.
$45,235
b.
$40,868
e.
$244,692.86
c.
$244,693
The price the machinery have initially cost rounded to the nearest dollar is $244,693
Exponential equationThe formula for calculating depreciation is expressed according to the formula:
P(t) = P0e^-rt
Given the following parameters
P(t) = $100,000
rate = 12% = 0.12
time =7 years
Substitute
100,000 = P0e^-(0.12)(7)
100000 = P0e^0.84
P0 = 100000/e^0.84
P0 = $244,693
Hence the price the machinery have initially cost rounded to the nearest dollar is $244,693
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Lock 4 (screen will be blank until you crack the code for lock #3) Awe-sum! You have reached the last lock. Use your equation solving skills to find the value of each variable. Use the values you calculate to help you move along in the puzzle and find all of the missing variables. When you have found all of the variables Imove to the next screen.
Problems:
4a +2= -10
a(2+ b) = -12
-5c+b= 22
7(c+d) = 14
d-c-e= 17
Answers:
a=
b=
c=
d=
e=
The values of the variables are:
a = -3
b = 2
c = -4
d = 6
e = -7
Given, the expressions are:
4a + 2 = -10
4a = -10-2
4a = -12
a = -3
substitute a value in the next expression.
a(2+b) = -12
-3(2+b) = -12
-6-3b = -12
-3b = -12+6
-3b = -6
b=6/3
b = 2
now substitute b value in the next expression.
-5c+b= 22
-5c+2 = 22
-5c = 22-2
-5c = 20
c = -20/5
c = -4
substitute c value in the next expression.
7(c+d) = 14
7(-4+d) = 14
-28+7d = 14
7d = 14+28
7d = 42
d=42/7
d=6
In the last expression substitute c and d values to find e.
d-c-e= 17
6-(-4)-e = 17
6+4-e = 17
10-e = 17
-e = 17-10
-e = 7
e = -7
hence we get the values of all the variables.
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gerber product's gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† if you want to provide your child with 300 calories and 74 grams of carbohydrates, how many servings of each should you use? gerber mixed cereal for baby serving(s) gerber mango tropical fruit dessert serving(s)
Number of servings of Gerber mixed cereal for baby = 1
Number of servings of Gerber mango tropical fruit dessert for baby = 3
Given information about Gerber products are,
Gerber mixed cereal for baby contains, in each serving, 60 calories and 11 grams of carbohydrates.
Gerber mango tropical fruit dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.
We have to find the number of servings of each to provide exactly 300 calories and 74 grams of Carbohydrates. So we need to find the appropriate combination of numbers 60 and 80 to make 300 and combinations of 11 and 21 to get 74.
Since 1 x 60 + 3 x 80 = 60 +240 = 300
and 1 x 11 + 3 x 21 = 11 + 63 = 74 ,
we can conclude that 1 serving of Gerber mixed cereal and 3 servings of Gerber mango tropical fruit dessert will do.
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5/6 x -4 1/2 x -2 1/5
Find the product. Write your answer as a fraction in simplest form.
Answer:
8 1/4 or 33/4
Step-by-step explanation:
How to muliply fractions: just multiply all the denominators together and the numerators together
However, if your mulitplying whole numbers, you have to change those into improper fractions using the formula: Whole number x denomiator + numerator
**Make sure to put the same numerator as you had before when you change to an improper fraction!!!
-4 1/2 = -9/2
-2 1/5 = -11/5
5 -9 -11 5 x -9 x -11 -45 x -11 (use a calculator) 495
-- x -- x --- = --------------- = ------------- = ------------
6 2 5 6 x 2 x 5 12 x 5 60
1 33
= 8.25 or 8 ---- = --------
4 4
there are 50 solidiers in a military camp. food provision for them is for 12 days, how long will their provision last if 10 more soldiers to win the camp (direct and inverse proportion)
Answer:
10 days
Step-by-step explanation:
60/50×12 give u the number of days it will last them
x^2y(7xy^4)
helppppp
− 2/ 3 is a/an . (check all that applies.) \sqrt{5} 5 is a/an . (check all that applies.) natural number integer rational number real number irrational number
The -2/3 is an integer and rational number.
It is required to choose the number.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given:
-2/3 is an integer and rational number.
The square root of 25 is 5 is an Natural numbers, whole number, integer, and rational number.
Natural numbers are positive whole numbers (1, 2, 3, 4, 5, ...)
Whole numbers are positive numbers start with zero (0, 1, 2, 3,...)
Integers are positive and negative whole numbers or zero (..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...)
Rational numbers include all integers as well as positive or negative numbers that have fractional parts ( -2.0, -3/4, 0.25, 2.1, 5, etc.)
Irrational numbers are numbers that can not be written as a simple fraction. Its decimal goes on forever without repeating (π = 3.14159....)
5 is a natural number, whole number, integer, and rational number.
Therefore, the -2/3 is an integer and rational number.
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Factor completely.
100-9x^2=
please help!!
Answer:
(10 + 3x) (10 - 3x)
Hope this helps!
1.) The weight of the tea in 100 identical tea bags is 8 ounces. What is the weight, in ounces, of the tea in 3 tea bags? Show your work.
Answer:
0.24 ounces for 3 teabags.
Step-by-step explanation:
Since this is a 1 digit number, we should find out how much each teabag weighs. We can do this by dividing 8 by 100, which gives us 0.08.
Now we can multiply that by 3, which gives us 0.24, so 3 teabags are 0.24 ounces.
What did Raya do wrong? Use complete sentences to describe her mistake.
During evaluation, Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.
How to Evaluate an Expression?Given the expression, a³ - b³ / 5, where:
a = 2
b = -3
Substitute the values into the expression
Step 1: (2)³ - (-3)³ / 5
Evaluate
Step 2: 8 - (-27) / 5 (this is where Raya made a mistake, she had -9 instead of -27)
Step 3: 8 + 27/5
Step 4: 35/5 [addition]
Simplify
Step 5: 35/5 = 5 [division]
Thus, we can state that Raya was wrong in step 2. She got the cube of -3 wrong. The correct value is -27 and not -9.
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Find the slope of the line through the
points (16,7) and (−14, 3).
Answer:
2/15
Step-by-step explanation:
Slope: m=(y2-y1)/(x2-x1)
m = (3 - 7)/(-14 - 16) = (-4)/(-30) = 4/30 = 2/15
a major disadvantage of correlations is that they cannot make a(n) blank statement. multiple choice question.
A major disadvantage of correlations is that they cannot make a cause-and-effect statement.
What are correlations?Correlations are statistical measures that describe the size and direction of a relationship between variables.
Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.
The disadvantages of correlations include:
There are no causes and effects.Results can find no inference.The strength of the relationship is not explained.There is the possibility of a confounding factor.Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.
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4. A regular pentagon has side lengths given below. Find the length of one side.
4q+1 = 11-q
r+s
s+t-1
3r
a) 9
b) 4
c) 3
d) 2
Answer:
d)2
Step-by-step explanation:
you would group-like terms and so
4q+q=11-1
5q=10(you would let q stand on it own)
so you divide through by 5
5q/5=10/5
q=2
Carla earned a total of $84 for 7 hours of babysitting. After a total of 8 hours of babysitting, how much money will Carla have earned? Assume the relationship is directly proportional.