Answer:
1/12 gallon per mowing12 mowings per gallonStep-by-step explanation:
Given that Angie can mow her lawn 4 times using 1/3 gallon of gas, you want to know how much gas is required for each mowing, and how many times Angie can mow on one gallon of gas.
Gallons per mowingTo find the number of gallons required for each mowing of the lawn, divide the number of gallons by the number of mowings:
(1/3 gal)/(4 mowings) = 1/(3·4) gal/mowing = 1/12 gal/mowing
It takes 1/12 gallon to mow the lawn once.
Mowings per gallonThe reciprocal of this value has the reciprocal units.
1/(1/12 gal/mowing) = 12 mowings/gal
Angie can mow the lawn 12 times with one gallon of gas.
__
Additional comment
It often proves useful to keep the units with the numbers when working rate problems. This can eliminate a lot of mistakes. The units are treated as you would treat a variable.
the scatter plot shows a regression line of units demanded and price. if the demand is for 35 units what would be the predicted price per unit?
A)$20
B)$23
C)$27
D)$32
According to the following graph, we have identified that if the demand is for 35 units then the predicted price per unit is $27.
The term graph in math is defined as pictorial representation of algebraic equation.
Here we have given the following graph and here we also know that the scatter plot shows a regression line of units demanded and price.
Here we need to know the definition of regression line, which means the relationship between two variables. And it is applied in scenarios where the change in the value of the independent variable causes changes in the value of the dependent variable.
Based on these definition, here we have the relationship between the units demanded and the price of those units.
Now, by looking into the given graph, we have identified that if the demand is for 35 units, then the units price is $27.
Therefore, option (c) is correct.
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Type the correct answer in each box. Use numerals instead of words. The length of a rectangular soccer field is 40 feet more than twice the width of the field. Complete an equation for the area of the field, where w is the width of the field.
A =2 w² +40 w
First Blank =2
Second Blank = 40
Here are several function rules. Calculate the output for rules 1–5 when you use -6 as the input for each rule. Simplify fractions and express in the form a/b if necessary and use the word pi for π
.
Answer: 13,36,-2,-2,pi
Step-by-step explanation:
You do exactly what it says for the rule to -6 to get your answer.
An isosceles triangle has an angle that measures 26°. Which other angles could be in that
isosceles triangle? Choose all that apply.
Answer:
26° 26° 128°
77° 77° 26°
Step-by-step explanation:
So we have two scenarios here.
One of them is if the base angles are 26°.
If that's true, the other angle is 128°
The other scenario is the opposite.
This means the base angles are 77°
Find 1)
4 integral 0 f(x) dx
if f(x) = 2 for x < 2
= x for x ? 2
Answer:
X = 1 and below
Step-by-step explanation:
since X is less than 2.
the value of X will be 1 and below.
road to white house Math
The value of f(4) - g(-5) if function f(x) = 3 / 2x + 2 and g(x) = 2x² - 3 is -39.
What is function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given:
f(x) = 3 / 2x + 2 and g(x) = 2x² - 3
Calculate the value of f(4) and g(-5) as shown below,
f(4) = 3 / 2 × 4 + 2
f(4) = 12 / 2 + 2
f(4) = 6 + 2
f(4) = 8
g(-5) = 2 × (-5)² - 3
g(-5) = 2 × 25 - 3
g(-5) = 50 - 3
g(-5) = 47
Now, calculate the value of f(4) - g(-5) as shown below,
f(4) - g(-5) = 8 - 47
f(4) - g(-5) = -39
Thus, the value of f(4) - g(-5) is -39.
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How many powers of 7 are contained in 10?
There is only 1 power of 7 contained in 10.
Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.
Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.
The digit in the tens place is the same.
The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.
The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.
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There is only 1 power of 7 contained in 10.
Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.
Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.
The digit in the tens place is the same.
The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.
The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.
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Does anyone know the question to this ?? :(
Answer:
The ratio of the new area to the old area will be 16:1
Step-by-step explanation:
I remember learning this in class. The radius is quadrupled, which means the radius is 4 times bigger. This will make the new area 16 times bigger than the old area.
Let's check
Area of circle: 3.14 x r^2
Area of the circle when radius 6:
3.14 (6)^2 = 113.04 ft^2
Area of the new circle when the radius is quadrupled:
3.14 (24)^2 = 1808.64 ft^2
1808.64 divided by 113.04 = 16
So, the ratio of the new area to the old area will be 16:1
9m-4n=1
11m-3n=5 in simontaneous equation
The values of the variables are n = -17/31 and m = 23/93
How to determine the valuesFrom the information given, we have the equations;
9m-4n=1 equation 111m - 3n = 5 equation 2To solve the simultaneous equation, we have to take the following steps
Make 'm' the subject from equation 1
9m = 1 + 4n
Divide both sides by 9, we get;
m = 1 -4n/9
Substitute the value into equation (2), we have;
11(1 -4n/9) - 2n = 5
expand the bracket
11 - 44n/9 - 2n = 5
find the LCM
11 - 44n - 18n /9 = 5
cross multiply
11- 62n = 45
collect like terms
-62n = 45 - 11
-62n = 34
Make 'n' th subject
n = -34/62
n = - 17/31
Substitute the value into equation (3)
m = 1 - 4(-17/31)/9
m = 1+68/31 ÷9
m = 69/31 × 1/9
m = 69/279
m = 23/93
Hence, the values are n = -17/31 and m = 23/93
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Find the x and y Intercept of x + 2y = -14
Answer:
Y-intercept: (0, -7)
X-intercept: (-14,0)
Step-by-step explanation:
To find the y-intercept, we need to put 0 in for x
0 + 2y = -14
2y = -14
y = -7
So, the y-intercept is located at (0, -7)
To find the x-intercept, we need to put 0 in for y
x + 2(0) = -14
x = -14
So, the x-intercept is located at (-14,0)
Step-by-step explanation:
To find the y-intercep, we need to put 0 in for x
0 + 2y= -14
2y = -14
y = - 7
So, the y - intercept is located at ( 0, - 7)
Brian sat in a massage chair at a shopping mall for 8 minutes and paid $9. Norah sat in
the same massage chair for 12 minutes and paid $11. If the relationship between the
number of minutes and the amount paid is linear, with x representing the minutes and y
representing the amount paid in dollars, which of these equations models the situation?
A. x = 0.5y + 5
B. x = y + 1
C. y = 0.5x + 5
D. y = x + 1
Answer:
(1/2)x + $5 (Answer A)
Step-by-step explanation:
Two points on the line representing the cost are (8, $9) and (12, $11).
The change in x is 4 (minutes); this is the 'run.' The change in y is $2 (this is the 'rise'). Thus, the slope of this line is m = rise / run = $2/(4 min), or 1/2 dollar per min.
Applying the slope-intercept formula y = mx + b, we get:
$9 = (1/2)(8) + b, and from this we see that b must be $5.
Then the correct equation is y = (1/2)x + $5.
Tamara said the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y). Is she correct? Explain. And what is the correct expression.
Answer:
Yes, Tamara is correct that the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y).
The Distributive Property states that for any real numbers a, b, and c, we have:
a(b + c) = ab + ac
This property allows us to distribute a factor to each term within a set of parentheses.
In this case, Tamara used the Distributive Property to rewrite the expression 21x + 56xy as an equivalent expression. She did this by taking the factor of 7 and distributing it to each term within the parentheses:
7(3x + 8y) = (73x) + (78y) = 21x + 56xy
Therefore, the correct expression is 7(3x + 8y).
Step-by-step explanation:
Live wants to have his birthday party at the bowling alley with a few of his friends but he must be a less than $80 the bowling alley charge a flat fee of $45 for a private party +5.50 per person
Answer: 45+16.5=61.5
Step-by-step explanation:
if there is 2 friends going with him it would be 45+16.5=61.5
so that is how much he spends in there is more friends ill give you the other answer if there is more friends
Factor quadratic trinomials
2x^2+7x+6
3x^2+5x+2
With method X pleaseee:(
Could someone please help me?
[tex]\textit{area of the rectangle}\\\\ A=Lw \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=5\\ w=6 \end{cases}\implies A=(5)(6)\qquad \begin{cases} \textit{tripling the sides}\\[-0.5em] \hrulefill\\ L=3\cdot 5\\ w=3\cdot 6 \end{cases} \\\\\\ A=(3\cdot 5)(3\cdot 6)\implies (3\cdot 3)(5)(6)\implies 9(5)(6)\leftarrow \begin{array}{llll} \textit{new area is 9 times}\\ \textit{the old one}\\ \textit{a ratio of 9 : 1} \end{array}[/tex]
What statements about prisms are always true if the top base is directly above the bottom base? Select all that apply. The lateral faces are rectangles. The bases are congruent. The bases can be any shape. The lateral faces are congruent.
Answer:
The bases are congruent
Step-by-step explanation:
From the question, we understand that the top base and the bottom base are directly opposite one another.
When such a scenario arise, it means that the bases have the same shape, they have the same dimension (i.e. size).
With the above analysis, we can conclude that the bases are congruent.
However, the given information can not be used to determine the shape and congruence of the lateral faces.
Lastly, for the bases to be congruent, they must have the same shape (and not any shape).
Hence, only option (b) is correct
In a random sample of 70 people, it was found that 44 of them were fans of the New York Yankees. What is the margin of error for the true proportion of all individuals who are fans of the New York Yankees? A. 0.0088 B. 0.058 C. 0.063 D. 0.116 E. 0.173
The margin of error for the true proportion of all individuals who are fans of the New York Yankees is 0.058.
The Correct option is (B).
How to find the margin of error?The formula to calculate the margin of error for the true proportion is;
M = √[p(1 - p)/n]
Given:
n= 40
p = 44/70
Now, The general formula for the margin of error would be:
z x √[p (1-p) ÷ n]
where:
z = values for selected confidence level
p = sample proportion
n = sample size
Since the confidence level is not given,
√[p (1-p) ÷ n]
=√[44/70 (1 - (44/70) ÷ 70]
=√[0.6286 (0.3714)] ÷ 70
=√0.2335 ÷ 70
= √0.0033357
= 0.05775 or 0.058
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WILL GIVE BRAINLIEST TO CORRECT ANSWER
In a group of 23 students, 2 study both Art and Biology.
2 study Biology but not Art.
4 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answer:
Total number of outcomes = 23
number of biology and art students = 2
number of biology students = 2
Since it is given that all the students study art,
number of possible outcomes = 2
probability = number of favorable outcomes/number of total outcomes.
= 2/23
Therefore probability that the selected student studies both art and biology is 2/23.
9 people audition for a choir. The choir director must choose one soprano, one alto,
and one tenor.
In how many ways can the director fill these positions?
The numbers of ways that the director fill these positions is 504 ways.
What is the position about?There are a few different ways to approach this problem, but one possible method is to use the combination formula.
To fill the position of soprano, the director has 9 choices. After selecting one soprano, the director is left with 8 singers to choose from for the alto position. Then, the director has 7 singers to choose from for the tenor position.
So, the total number of ways the director can fill these positions is:
9 × 8 × 7
= 504 ways.
Alternatively, One can also use the permutation formula to solve the question. The formula of permutation is (n!/(r!(n-r)!)), where n is the total number of items to choose from, and r is the number of items to be chosen.
For this case n is 9, and r is 3, so the permutation would be:
(9!/(3!(9-3)!)
= (987)/(321)
= 504
Therefore, In both cases, the answer is 504 ways.
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A gift box in the shape of a rectangular prism has 20-inch length, 14-inch width, and 10-inch height. How much paper will you need to wrap the gift box?
Answer:
1240 in²Step-by-step explanation:
Total surface area:
S = 2(lw + lh + wh)S = 2(20*14+20*10+14*10) = 1240 in²So
TSA
2(LB+BH+LH)2(20×14+14×10+10×20)2(280+140+200)2(620)1240in²Kelvin and Lewie each design surveys in order to determine the average number of people who buy food at the mall. Kelvin surveys every other person leaving the food area. Lewie surveys every fifth person leaving the mall main entrance. Which set of survey results is most likely to show biased results for people who buy food at the mall
The set of survey results that is most likely to show biased results for people who buy food at the mall is Lewie's survey.
Lewie's survey samples only every fifth person leaving the mall's main entrance, which means that it only captures a small percentage of the total number of mall visitors. Additionally, by only surveying people leaving the main entrance, Lewie's survey may not capture people who enter and exit the mall through other entrances or exits and may also miss those who don't leave the mall after buying food. As a result, Lewie's survey may not accurately represent the total number of people who buy food at the mall and may lead to biased results.
On the other hand, Kelvin's survey samples every other person leaving the food area. This method captures a larger percentage of the total number of people who buy food at the mall and is more likely to provide a more accurate representation of the total number of people who buy food at the mall.
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Answer:
A. Kelvin’s because he surveyed people leaving an area where food is sold
Step-by-step explanation:
Yesterday, Jake ran 2 1/2 miles in 3/5 hour. Lance ran 3 3/4 miles in 5/6 hour. Who ran fastest?
Answer:
jake did :)
Step-by-step explanation:
hope this helps ! <3
Lance is fastest because the speed of the Lance is 4.5 miles/hour and Jale speed is 4.16 miles/hour as 4.5>4.16
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Jake ran = [tex]2\frac{1}{2}[/tex] miles = 5/2 miles
In 3/5 hours
Thespeed = (5/2)/(3/5) = 4.16 miles/hours
Lance ran = [tex]3\frac{3}{4}[/tex] miles = 15/4 miles
In 5/6 hours
The speed = (15/4)/(5/6) = 4.5 miles/hours
Thus, Lance is fastest because the speed of the Lance is 4.5 miles/hour and Jale speed is 4.16 miles/hour as 4.5>4.16
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The table below shows information about how many fans there were at two
football matches in a local tournament.
What is the difference between the number of away fans at the semi-final and at
the final?
Semi-final
Final
Total number of fans
250
400
Ratio of home fans
to away fans
6:4
7:3
Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).
What is ratio?A ratio or fraction in math displays how many times one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3 or decimal 1.333).
Here,
Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.
A statistical data's confidence interval can be expressed as.
=> x+/-zr/√n
=> Knowing that;
Average Sample x = $70.00
$17.50 is the standard deviation.
n = 60 samples were used.
95% confidence interval
95% confidence interval for z = 1.96
substituting our current values;
$70.00+/-1.96($17.50/√60)
$70.00+/-1.96($2.259240285287)
$70.00+/-$4.428110959163
$70.00+/-$4.43
= ( $65.57, $74.43)
Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).
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Evaluate the following expression: (-5)(6) + (-6) ÷ (-3). Remember to show your work
Answer:
-28
Step-by-step explanation:
(-5)(6) + (-6) ÷ (-3) =
-30 + (-6) ÷ (-3) =
-30 + 2 =
-28
Hope that helps! :)
-Aphrodite
Answer: =-28
Step-by-step explanation: Hope this help :D
Mashika: We already know from polling data that some segments of the electorate provide significant support to Ms. Puerta. If those segments also provide significant support to Mr. Quintana, then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez.
Salim: But actually, as the latest polling data conclusively shows, at least one segment of the electorate does provide significant support to both Mr. Quintana and Mr. Ramirez.
Among the following statements, which is it most reasonable to infer from the assertions by Mashika and Salim?
A. At least one segment of the electorate provides significant support neither to Mr. Quintana nor to Mr. Ramirez.
B. At least one segment of the electorate provides significant support to Ms. Puerta but not to Mr. Quintana.
C. Each segment of the electorate provides significant support to Ms. Puerta.
D. Each segment of the electorate provides significant support to Mr. Quintana.
E. Each segment of the electorate provides significant support to Mr. Ramirez.
Answer:
D. Each segment of the electorate provides significant support to Mr Quintana
Step-by-step explanation:
From the question, we have the following logic statement;
If those segment that provide significant support to Ms Puerto also provide support to Mr. Quintana then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez
Counter to the If Then Logic structure
At least one segment of the lectorate provides significant support to Mr. Quintana and Mr. Ramirez
Therefore, there is at least one segment that provides support to Mr. Quintana but not to Ms. Puerta
The segments that provide support to Ms. Puerta do not provide support to Mr. Ramirez
Mr. Quintana's support includes those from the supporters of Ms. Puerta and those from the supporters of Mr. Ramirez
Therefore, each segment of the electorate provide significant support to Mr. Quintana.
3 chairs and 4 tables cost rs 7540. if the price of a chair is 220 find the price of table?
ans - 7120
Answer:
The price of a table is rs1720
Step-by-step explanation:
Let C and T be the individual prices of the tables and chairs.
We know that 3C + 4T = rs7540
We are then told that C = rs220, so we can enter that into the equation to find T:
3C + 4T = rs7540
3(220) + 4T = rs7540 [for C = rs220]
660 + 4T = 7540
4T = rs6880
T = rs1720
Check:
Do 3 chairs at 220 each and 4 tables at 1720 each add to a total of 7540?
Chairs: rs660
Tables: rs6880
Total = rs7540 YES
what is -5.6 opposite ?
Answer: 5.6
Step-by-step explanation:
the opposite of an negative number...
So your answer would be....
=5.6
Answer:
[tex]5.6[/tex] or [tex]\dfrac{1}{-5.6}[/tex]
Step-by-step explanation:
The additive inverse of [tex]-5.6[/tex] is [tex]-1 \cdot -5.6 = \boxed{5.6}[/tex]
or...
If you mean the multiplicative inverse of [tex]-5.6[/tex], then the answer would be [tex]\dfrac{1}{-5.6}[/tex]
Solve these problems
A= 12+4×2-7
B= 2×(-3)+8
Answer:
A. 13
B. 2
Step-by-step explanation:
You use order of operations.
A. 4x2=8+12=20-7=13
B. 2x-3=-6+8=2
How do you graph a parent graph?
This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.
For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola. For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
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What is the degree of the polynomial 7x 3 4x² *?
The degree of polynomial 7x³ + 4x² is 3 as the highest power is 3.
What is degree of polynomial?One of the fundamental ideas in mathematics is the degree of polynomials, which determines the maximum number of solutions a function can have and how frequently a function will cross the x-axis on a graph.
Polynomials are also useful in understanding how functions can be represented mathematically. It has the highest exponential power in the polynomial equation.
The greatest power of a variable in a polynomial equation is its degree. When calculating the degree of a polynomial function, only terms with variables are considered. The degree of the polynomial can be determined by looking at the variable term with the highest exponential power.
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