Answer:
To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 miles. We are told that the car used \frac{2}{5} 5 2 of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 to get the total number of gallons used:
\frac{2}{5} \cdot 15\tfrac{1}{2} = 9
Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:
15\tfrac{1}{2} \div 9 = \frac{31}{18}
This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:
\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}
Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:
\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}
Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.
Justin is going to invest $90,000 and leave it in an account for 19 years. Assuming
the interest is compounded quarterly, what interest rate, to the nearest hundredth of
a percent, would be required in order for Justin to end up with $216,000?
Answer:
4.63%
Step-by-step explanation:
You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.
Compound interestThe formula for the balance of an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
ApplicationFilling in the given values, we can solve for r:
216000 = 90000(1 +r/4)^(4·19)
2.4 = (1 + r/4)^76 . . . . . divide by 90,000
2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root
(2.4^(1/76) -1) = r/4 . . . . . . subtract 1
r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%
The required interest rate is about 4.63%.
What is an equation of a line that passes through the points (1, 4) and (2, 9) in
5)
point-slope form? Analyze the steps and fill in the blanks. (4pts)
First, use the two given points to find the slope.
m=
Уг-У1
Use the slope and one point to write an equation of the line in
point-slope form.
Point-slope form of a linear equation.
Substitute
The equation of line in point-slope form of the line, is y = 5x - 1.
What is point - slope form of the line?
The general form of a linear equation is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
The line passes through the points (1, 4) and (2, 9).
We have to find the equation of line in point - slope form.
First to find the slope from the given points.
Since,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]
So, [tex]m = \frac{9-4}{2-1} = 5[/tex]
Now consider, the point slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]
⇒
[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]
Hence, the equation of line in point-slope form of the line, is y = 5x - 1.
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7x+14y=21,-7x+7y=7 using elimation
Answer:(x,y)=(1/3 , 4/3)
Step-by-step explanation:
Write the coordinates of the vertices after a reflection over the line y=-5.
The coordinates of the vertices after a reflection over the line y = -5 is given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
How to obtain the coordinates of the vertices after the reflection?The vertices of the original quadrilateral are given as follows:
T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).
The reflection line y = -5 is an horizontal line, meaning that after the reflection:
The x-coordinate remains constant.The y-coordinate will be equidistant to y = -5, however in an opposite direction.For example, the distance of the y-coordinate of the vertex U from -2 is of:
2 units above.
Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:
U'(2,-7).
Applying this rule for all the other vertices, they will be given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
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read the picture plsss
Answer:
Step-by-step explanation:
Solve for c.
4(c + 17) = 16
C =
Please help
a company makes wax candles in the shape of a cylinder. each candle has a diameter of 4 inches and a height 8 of inches. if the company used of wax, how many candles did it make? use for , and do not round your answer.
If the company has made 6732.16 in³ wax , Total number of candles made is 67
According to the question,
It is given that a wax candle is in cylindrical shape
Diameter of candle = 4 in
Radius will be = 4 / 2
=> 2 in
Height of each candles = 8 in
Company has used 6732.16 in³ of wax
We have to calculate number of candles company has made
Volume of cylinder = πr²h
Where r is radius and h is height
Substituting all the values,
Volume of candle = π (2)² (8)
=> V = 3.14 × 4 × 8 (putting π = 3.14)
=> V = 100.48
Therefore , Number of candles made = Total volume /volume of one candles
=> 6732.16 / 100.48
=> 67 candles are made by company
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What is the value of 24 + x ÷ 12 when x = −180?
17
9
−13
−178
If you don't know the answer please do not type random stuff or you'll see what ima do
The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?From the question, we have the following parameters that can be used in our computation:
24 + x ÷ 12
Also, we have the value of the variable to be
x = −180
Substitute the known values in the above equation, so, we have the following representation
24 - 180 ÷ 12
Evaluate the quotient in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 24 - 15
Evaluate the difference in the above equation
So, we have the following representation
24 - 180 ÷ 12 = 9
Hence, the value of the expression is (b) 9
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Simplify 4x - 7 + 12x - 3.
Answer:2(8x-5)
Hope this helps!
a vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a
A vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a two factor chi Square test.
The Pearson chi-square (χ²) test, often simply called the chi-square test, is one of the most common non-parametric tests. Nonparametric tests are used for data that do not follow the assumptions of parametric tests, especially the assumption of normal distribution.
To test hypotheses about the distribution of a categorical variable, you should use the chi-square test or another non-parametric test. Categorical variables can be nominal or ordinal and represent groups such as species or nationality. They can only have a small number of specific values, so they cannot have a normal distribution.
Bidirectional chi-square is one of several tests of goodness of fit between the actual values of two nominal or ordinal variables and the values expected if the variables were unrelated or independent. Chi-square is also known as Pearson Chi-square and Chi-square test of independence. The symbol for the chi-square test is the lowercase Greek letter chi (χ) with a superscript 2, such as χ2. χ2 is a test of significance and should be accompanied by an appropriate test of strength. The strength test should be chosen based on the number of rows and columns in the table of observations. In particular, one of the most commonly used strength tests is the π coefficient.
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AB and CD bisect each other at E m/CAE 80 and m/BDE 60 Amy says that mZCEA = 20°, Brent says that it is 30", Carlos says that it is 40", and Debra says that it is 50" Which
student is correct?
The only person that is correct with respect to the measurement of ∠CEA of the congruent triangles is; Carlos
How to Interpret Congruent Angles?From the diagram attached, we are given that;
The measure of ∠CAE = 80°
∠BDE = 60°
Amy says that m∠CEA = 20°
Brent says that it is 30°
Carlos says that it is 40°
Debra says it is 50°
Now, by inspection, it is clear that ΔCAE is congruent to ΔBDE by SAS Congruency postulate and as such we can say that;
∠A = ∠B and ∠C = ∠D
Thus;
∠B = 80° and ∠C = 60°
Sum of angles in a triangle is 180 degrees and so;
∠CEA = 180 - (80 + 60)
∠CEA = 180 - 140
∠CEA = 40°
Which means that Carlos is correct.
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
The solution of the given expression is equal to 2.17.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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What i cot of tiling a rectangular plot of land 500m long and 200m wide at the rate r 8 per q m
The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
Area of rectangle = length × breadth
Area of rectangular plot = 500× 200 = 1,00,000 sq m
Cost of tilling 1 sq m of land = Rs. 8
Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000
Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
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suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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Which equation, when paired with y = 2x 5, creates an inconsistent system? 2x y = 5 y = 2x 5 2x – 4y = 10 2y – 4x = –10
The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:
2y - 4x = -10.
What is an inconsistent system?A system of equations is called inconsistent when the number of equations of the system is of zero.
The system in this problem is composed by linear equations, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For inconsistent system, we have that the equations:
Have the same slope.Have different intercepts.The function in this problem is given as follows:
y = 2x + 5.
Hence the inconsistent system is formed with:
2y - 4x = -10.
Which is simplified by 2 as follows:
y - 2x = -5.
y = 2x - 5.
Having the same slope of 2, but a different intercept.
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Answer: 2y – 4x = –10
Step-by-step explanation: trust.
What is the radius of the circumscribed circle of ABC?
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
:]
Sadie is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Sadie will earn $40 every time one of her songs is played in a commercial and she will earn $120 every time one of her songs is played in a movie. Sadie's songs were played on 3 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $440. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Sadie's songs were played. Define the variables that you use to write the system.
The number of commercials and movies on which the songs were played are 5 and 2.respectively
How to determine the number of commercials and movies on which the songs were played.From the question, we have the following parameters that can be used in our computation:
Earnings from songs played in commercial = $40Earnings from songs played in movie = $120Total earnings = $440The number of commercials is x, and the number of movies is y
The above parameters when represented as an equation is as follows
40x + 120y = 440
x = y + 3
Substitute x = y + 3 in 40x + 120y = 440
40(y + 3) + 120y = 440
Expand
40y + 120 + 120y = 440
Evaluate the like terms
160y = 320
Divide by 160
y = 2
Recall that
x = y + 3
So, we have
x = 2 + 3
x = 5
Hence, the number of commercials is 5 times
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If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value. 17. f[g(–2)]
a. 7 b. 10 c. 30 d. 100
Answer:
d.) 100
Step-by-step explanation:
To solve, first find the value of g(-2):
[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]
Next, use this value to find f(-10):
[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]
Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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21. Is the following ordered pair (3, 6) a solution of the linear inequality y < -5x + 1?
The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
What is linear inequality?
A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
y < -5x + 1
Substitute the points and see if they are true
(3, 6)
6 < -5*(3) + 1
6 < -15 + 1
6 < -14
Not true not a solution
Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
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The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
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6x-7=1-3x[tex]6x-7=1-3x[/tex]
Answer:
x=8/9
Step-by-step explanation:
step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.
3x+-3x cancels itself out and 3x+6x=9x.
now, the equation looks like: 9x-7=1
step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.
7+-7 cancels itself out and 7+1=8.
now, the equation looks like 9x=8
step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".
9x/9= x, 8/9
so the answer is x=8/9
hope this helped!!
If Santa Claus ate two cookies from every child on Earth, how many cookies would he eat over one Christmas Eve?
Answer:
three billion eight hundred million
Step-by-step explanation:
how is (-7.5)-21.04 and (-7.5)+21.04 the same value?
The values (-7.5)-21.04 and (-7.5)+21.04 are not the same
What is a decimal?A decimal can be defined as a number consisting of a whole number and also a fractional part.
These numbers are separated by a dot known as the decimal point
The decimal numeral system is seen as a standard system that denotes integer and non-integer numbers.
It is important to note the following operations;
+ × + = ++ × - = -- × + = -- × - = +From the information given, we have;
(-7.5)-21.04
Multiply the operation
+ 157. 8
Then,
(-7.5)+21.04
Multiply the operation
- 157. 8
Hence, the values are either negative or positive.
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Deposited (dollars)
12,500
10,000
7,500
$5,000
rate of change=
2,500 initial value=
Time (years)
y
dollars per year
dollars
The rate of change is $2500 per year.
The initial amount is $5000.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
In the given graph,
The initial value that deposited at x = 0 is $5000.
To find the rate of change in amount per year,
Find slope of the line, because rate of change will be equal to slope.
Let two points are (0, 5000) and (1, 7500)
The slope = (7500 - 5000 / 1 - 0) = 2500
The rate of change is $2500 per year.
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x^4-2x^2-16x-15=0 find the zeros with work please
ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)
steps
find the zeros JUST MEANS SOLVE FOR X
x⁴-2x²-16x-15=0
break it up
let u = x²
x⁴ = (x²)² = u²
-16x+u²-2u-15=0
hold off on -16x
u²-2u-15=0
what 2 numbers when multiplied give you -15 & when added give you -2?
-5 and 3
(u-5) (u+3)
-16x + (u-5) (u+3) = 0
go back x
-16x + (x²-5) (x²+3) = 0
factor -1 out
( looks horrible so far lol )
-1 ((- x²+ 5) (x²+3) + 16x) = 0
multiply (- x²+ 5) with ( x² + 3 )
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0
-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0
Find the y intercept y = – 17 x + 12.
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
for what values of x and y are the triangles congruent by HL?
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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a study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. one hundred participants are recruited to participate, and half are randomly assigned to participate in the intervention while the others serve as a control group. what study design is being used?
A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).
What is a randomized controlled trial?Generally, In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.
In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.
The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.
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One of the tallest ferris wheels in the world is in las vegas. It has a diameter, , of 520 feet. The circumference of the ferris wheel represents the distance traveled by a passenger after one full rotation. The circumference can be determined using the expression. What is the distance traveled, in feet, by passengers on each rotation of the ferris wheel? record your answer to the nearest tenth of a foot.
Answer:
Below
Step-by-step explanation:
Circumference of a circle = pi * diameter
circumference of ferris wheel = 3.14159 * 520=1633.6 ft
