Simplifying the expression, we have:
[tex]\begin{gathered} (9x+3)-(5x-7) \\ =9x+3-5x+7 \\ =(9x-5x)+(3+7) \\ =4x+10 \end{gathered}[/tex]So the simplified expression is 4x + 10.
If f(x) = x^4 − x^3 + x^2 and g(x) = −x^2, where x ≠ 0, what is (f ⁄g)(x)?
The correct answer is
[tex](\frac{f}{g})(x)=-x^2+x-1[/tex]To solve this, first let's write the division:
[tex]f(x)=x^4-x^3+x^2,g(x)=-x^2\Rightarrow(\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}[/tex]Now we can factor out a x^2 on the top and the bottom of the expression:
[tex](\frac{f}{g})(x)=\frac{x^4-x^3+x^2}{-x^2}\Rightarrow(\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}[/tex]Now we can cancel out and divide by (-1), or the same thing, multiply by (-1):
[tex](\frac{f}{g})(x)=\frac{x^2(x^2-x+1)}{x^2(-1)}=-(x^2-x+1)=-x^2+x-1[/tex]Then the answer is (f/g)(x) = -x^2 + x - 1. That's the third option
BRAINLIEST (statistics) (please help fast)
The fuel economies in miles per gallon (mpg) for nine vehicles are listed below.
16, 18, 20, 24, 24, 24, 24, 31, 32
If one more vehicle is added to the list with a rate of 40 mpg, how will this affect the mean and median?
The mean and median will both increase.
The mean will increase and the median will decrease.
The mean will increase and the median will not change.
The mean will decrease and the median will not change.
Considering the concepts of the mean and the median, the correct option regarding the addition of one more vehicle is given by:
The mean will increase and the median will not change.
What are the mean and the median of a data-set?The mean of a data-set is obtained as the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.
Hence, for the given data-set, the mean is:
M = (16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32)/9 = 23.67.
Hence, if we add a value greater than the mean to the data-set, the mean will increase. In this problem, a rate of 40 mpg would be greater than any observation in the data-set, thus also greater than the mean, which would increase. The new mean is shown as follows:
M = (16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 + 40)/10 = 25.3.
The median of a data-set is the middle value of the data-set, the value which 50% of the observations are less than and 50% are greater than. Hence, the addition of an extreme value, such as 40 mpg in the context of this problem, does not change the median of the data-set.
For the original data-set, the median is:
24
As the data-set is divided into two halfs:
First: 16, 18, 20, 24.Second: 24, 24, 31, 32.With the new element, the halfs would be given by:
First: 16, 18, 20, 24.Second: 24, 24, 32, 40.The median would be the mean of the two middle elements of 24, hence:
Median = (24 + 24)/2 = 24.
Since the mean increases and the median remains constant, the third option is correct.
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a rectangles width is 11 feet more than its length if the perimeter is 54 feet what is the length and width?
Let the length of the rectangle be l and the width be w
width is 11 feet more than length: we can write:
w = 11 + l
Also , perimeter is 54, we can write:
2l + 2w = 54
Note: Perimeter is sum of all sides
Now,
we replace 1st equation in 2nd and find l:
[tex]\begin{gathered} 2l+2w=54 \\ 2l+2(11+l)=54 \\ 2l+22+2l=54 \\ 4l=54-22 \\ 4l=32 \\ l=\frac{32}{4} \\ l=8 \end{gathered}[/tex]w is 11 + l
So,
width is 11 + 8 = 19
Length = 8 feet
Width = 19 feet
Belinda is altering dance costumes for an upcoming recital. The number of costumes
she can alter varies directly with the amount of time spent working. If Belinda can
alter four costumes in one hour, find the number of costumes she can alter in four
and a half hours.
Answer: c
Step-by-step explanation: the equation asks for the divison of the two equal libruims and u subtract the numeriator by the scound stance
is (8, -44) a solution of the equation y = -7x + 6?
The ordered pair (8, -44) is not a solution of the equation
How to determine the true statement?The equation of the function is given as
y = -7x + 6
The possible solution of the equation is given s
(8, -44)
This means that
x = 8 and y = -44
Substitute x = 8 and y = -44 in the equation y = -7x + 6
So, we have the following equation
-44 = -7 x 8 + 6
Evaluate the products
So, we have the following equation
-44 = -56 + 6
Evaluate the sum
So, we have the following equation
-44 = -50
The above equation is false
Hence, the solution is not a solution
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Fred has 5/8 of a pizza left to share with 3 people. If it is split up evenly, how much of the pizza will each person get?
9. Higher Order Thinking The table shows
the temperatures of the water in
14 different beakers. What is the average
temperature, rounded to the nearest tenth
of a degree?
Temperatures in Beakers
Temperature 4.5°C 3.7°C 4.3°C 4.1°C 2.9°C
Frequency
3
4
2
3
2
The Average temperature of the given distribution is; 3.3°C
What is the average temperature?When given the values of the input and their frequencies of occurrence, the average mean can be calculated from the formula;
x' = ∑fx/∑f
Thus;
∑fx = ((4.5 * 3) + (3.7 * 4) + (4.3 * 2) + (4.1 * 3) + (2.9 * 2))
∑fx = 13.5 + 14.8 + 8.6 + 12.3 + 5.8
∑fx = 46.4
∑f = 3 + 4 + 2 + 3 + 2
∑f = 14
Thus;
Average temperature = 46.4/14 = 3.3°C
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What is the slope of the line through the point (4,4p) & (10,12q)?
(hint: Use the slope formula)
Answer: slope =4/3
Step-by-step explanation:
y2 - y1 / x2 - x1
y2 = 12
y1 = 4
12 - 4 / x2 - x1
subtract: 8 / x2 - x1
x2 = 10
x1 = 4
8 / 10 - 4
subtract: 8/6
8/6 simplify to 4/3
The slope is 4/3
Robert has attended 32 out of 40 soccer practices this year. Based on his record of attendance, which is
the probability that Robert will attend soccer practice in the future?
Step-by-step explanation:
he attended 32 of 40.
that was a rate
32/40 = 4/5 = 0.8
if he keeps the same ratio, then the probability for him to attend any soccer practice in the future is 0.8.
If f(x) = -2x^2 + 6 and g(x) =3xm evaulate the expressions below:
a. f(-1) + g(4)
b. 2g(2) - 7
Answer:
a
Step-by-step explanation:
Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
o Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
o Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)
What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev) /
If the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
Given that the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows.
We are required to find the margin of error of Val's data.
Margin of error is basically the difference between the actual data and the calculated data.
Margin of error=1.96*σ/[tex]\sqrt{n}[/tex]
In our case σ=50 and n is 100.
Margin of error=1.96*50/[tex]\sqrt{100}[/tex]
=1.96*50/10
=1.96*5
=9.80
Hence if the average weight found by Val is 1380 pounds with standard deviation 50 of 100 cows, then Val's margin of error will be 9.80.
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Evaluate sin 315º without using a calculator.O A. 132DIRO B.B. -12OC, V22O D. - 12
Answer:
Choice D.
Explanation:
Another way to write 315 degrees is
[tex]315-360=-45[/tex]In other words, when measured clockwise, 315 degrees = -45 degrees; therefore, our problem becomes
[tex]\sin 315^o=\sin -45^o[/tex]since
[tex]\sin \theta=-\sin -\theta[/tex][tex]\sin 45=-\sin -45[/tex][tex]\frac{\sqrt[]{2}}{2}=-\sin -45[/tex][tex]\sin -45=-\frac{\sqrt[]{2}}{2}[/tex]Therefore,
[tex]\boxed{\sin 315^o=-\frac{\sqrt[]{2}}{2}}[/tex]which is our answer!
5. Using p and q below, write the symbolic statement in words. Assume that p and q are true. q: 3x + 2 = 14 p: the value of x is 4
p⇒ q
~p ~q
q→p
~q→ ~p
In order to avoid ambiguity, symbolic logic represents logical expressions by substituting symbols and variables for natural language, such as English. Statements with a truth value, or whether they are true or untrue, are referred to as logical expressions.
How should a symbolic message be written?
A letter, such as p, can represent a whole proposition in symbolic logic. For instance, it might symbolize the fact that a triangle has three sides. The plus sign in algebra connects two numbers to create a third number. In symbolic logic, a sign like the letter V joins two propositions to create a third one.
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24 lemons are required to make 32 gallons of lemonade. How many lemons are needed to make 4 gallons of lemonade?
Answer:
Step-by-step explanation:
Simple:
24:32
?:4
This means just divide by 8 to get four. This also means to divide 8 for 24 also
24/8:4=
3:4 as answer
In a circle, the perpendicular bisector of a chord contains the center of the circle.Given : O X with L the 1 bisector of WY.Prove: L contains the center of O X.
All radii of the circle are congruent.Therefore, the radii XW and XY are congruent
[tex]\begin{gathered} XW\cong XY \\ \end{gathered}[/tex]Help please thanks please. Solve for the value of d to the nearest tenth place
d = √74
d = 8.6 (to the nearest tenth place)
Explanations:Given the expression to calculate the distance between the coordinates (-2, 1) and (5, -4) as shown:
[tex]d=AB=\sqrt{(5-(-2))^2+(-4-1)^2}[/tex]Simplify
[tex]\begin{gathered} d=\sqrt{(5+2)^2+(-5)^2} \\ d=\sqrt{7^2+5^2} \\ d=\sqrt{49+25} \\ d=\sqrt{74} \\ d\approx8.6 \end{gathered}[/tex]Hence the simplified form of the expression is √74 or 8.6
The side view of a tire resembles a doughnut. If the inner diameter is 11.0 in. and the out diameter is 25.0 in., what is the area (in square inches) of the side of the tire?
If the side view of a tire resembles a doughnut. If the inner diameter is 11.0 in. and the out diameter is 25.0 in., Then area of the side of tire is 92237.5 inches.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
A doughnut is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
A doughnut has two circles. One circle with in the other circle.
The diameter of inner circle is 11.
So radius of inner circle is 5.5 inches.
The diameter of outer circle is 25 inches.
The outer circle add diameter of inside circle.
25+11=36 inches.
The radius of outer circle is 18 iches.
The area of doubtnut
Area of big circle - Area of small circle or inner circle
Area of doubtnut= πR²-πr²
R outer radius= 18
r inner radius =5.5
Area of doubtnut= 3.142 (R²-r²)
=3.142(18²-5.5²)
=3.14(324-30.25)
=3.14(293.72)
=92237.5 inches
Hence the area of the side of the tire is 92237.5 inches
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Find the volume of this figure
Answer: 704 ft^3
Step-by-step explanation:
8 ft x 8 ft x 8 ft = 512 ft^3
(8 ft x 8ft x 9 ft)/3 = 192 ft^3
512 ft^3 + 192 ft^3 = 704 ft^3
i need better help understanding slope like how do i find the point on the graph
Solution
The slope of a straight line can be found from any graph by first drawing a triangle against the straight line indicating the rise and the run
The triangle usually is gotten by drawing straight lines from points on the graph where the line passes exactly across the intersection of lines of the y-axis and the x-axis
The circled points are good for usage to get the slope because the line passes exactly at the intersection of the vertical and horizontal line of the graph
Below is how the triangle will look
'The equation for the slope then is written as
[tex]\text{slope = }\frac{y_2-y_1}{x_2-x_1}=\frac{rise}{run}[/tex][tex]\begin{gathered} \text{From the graph as indicated} \\ y_2=8 \\ y_1=2 \\ x_2=\text{ 4} \\ x_1=2 \end{gathered}[/tex]Therefore the slope after substitution is
[tex]\begin{gathered} \text{slope = }\frac{8-2}{4-2} \\ \text{slope}=\frac{6}{2} \\ \text{slope = 3} \end{gathered}[/tex]The slope = 3
help meeeeeeeeee pleaseee
Inequalities define the relationship between two non-equal values. Inequality means being unequal.
option C is the correct Graph.
Relation { x | -7 < x < 3} .
solution in interval notation ( -7 , 3 ) .
Why do we study inequalities?To comprehend inequality, one must first comprehend the modern world and the forces that shaped it. More specifically, understanding inequality is a prerequisite for overcoming it: that is, for healing past wounds, generating social solidarity, and rebuilding a more just society.According to experts, inequality stifles economic growth and fosters political dysfunction. Because rich households spend less of their income than poorer households, concentrated income and wealth reduces the level of demand in the economy. Reduced opportunities for low-income households can also have a negative impact on the economy.To learn more about : Inequality,
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which ratio is equivalent to 1 and 8 a.7 to 14b. 7 to 9c.6 to 41d.6 to 48
we can see that
[tex]\frac{6}{48}=\frac{6}{6\cdot8}=\frac{1}{8}[/tex]hence, the answer is d).
A typical passenger vehicle emits about 4.7 metric tons of carbon dioxide per year. Assuming there are 253 million cars and trucks in the U.S, estimate the total emitted weight of carbon dioxide in the U.S
To estimate this quantity we can multiply the quantities given in the problem:
[tex]253\cdot4.7=1189.1[/tex]The estime total emmited weight of carbon dioxide in the U.S. is about 1189.1 millions of tons
please help me!!!!!!
This is a table that models the data correctly, and the percentage is 21.52%.
It's calculate of this way:
[tex]\frac{100}{79}\cdot17=21.52[/tex]What is the zero of p(x) = ax-b ?
Given:
[tex]p(x)=ax-b[/tex]Let p(x)=0
[tex]\begin{gathered} 0=ax-b \\ ax=b \\ x=\frac{b}{a} \end{gathered}[/tex][tex]\frac{b}{a}\text{ is the zero of p(x)}[/tex]What is x^2+x when x = 69?
if x = 69, then x^2+x = 4830
sovle the equation 8x-11=9x+2
Given the equation:
[tex]8x-11=9x+2[/tex]To solve this equation for x, the first step is to pass the x-term to the left side of the equation and the number to the right side. For this, you have to apply the opposite operation to both sides of the equal sign, that is, to subtract 9x and to add 11:
[tex]\begin{gathered} 8x-9x-11=9x-9x+2 \\ -x-11=2 \end{gathered}[/tex][tex]\begin{gathered} -x-11+11=2+11 \\ -x=13 \end{gathered}[/tex]Note that the x-term is negative, but the objective is to determine the value of x, so we have to multiply it by (-1) to reverse its sign, and to keep the equality valid, you have to multiply both sides of the equation by (-1)
[tex]\begin{gathered} (-1)(-x)=(-1)\cdot13 \\ x=-13 \end{gathered}[/tex]Which situation is the best modeled by a nonlinear function with time as the independent variable?
The most accurate model for a quadratic regression is a nonlinear function with time as the independent variable.
A non-linear relationship between the independent and dependent variables is stated in the regression model.
Along with the independent variable's square, it also contains the dependent variable.
The equation is Y=ax²+bx+c
When the independent variable is called x, and the dependent variable is called y.
Here, a, b, and c are the constant variable.
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how many 725ml is in liters?
ANSWER
There are 0.725L in 725mL
EXPLANATION
Given that
The volume in mL is 725mL
Follow the steps below
Recall, that 1mL is equivalent to 0.001L
Let x represents the volume in Liters
[tex]\begin{gathered} \text{ 1mL }\rightarrow\text{ 0.001L} \\ \text{ 725mL }\rightarrow\text{ xL} \\ \text{ cross multiply} \\ \text{ 1mL }\times\text{ xL = 725mL }\times\text{ 0.001L} \\ \text{ isolate xL} \\ \text{ xL = }\frac{725\cancel{mL}\times\text{ 0.001L}}{1\cancel{mL}} \\ \text{ xL = 725 }\times\text{ 0.001} \\ \text{ x = 0.725L} \end{gathered}[/tex]Therefore, there are 0.725L in 725mL
The Earth has an eccentricity of 0.017. Which of the three ellipses that you calculated do you think is the most similar in eccentricity to the Earth’s orbit? Why?
SOLUTION
Eccentricity means a measure of how much the deviation of the curve has occurred from the circularity of the given shape.
Of the three ellipses, the eccentricity is
[tex]\begin{gathered} \text{Ellipses 1=0.21} \\ \text{Ellipses 2=}0.4 \\ \text{Ellipses 3=0.64} \end{gathered}[/tex]Ellipses 1 has an eccentricity closer to the eccentricity of the Earth
Hence
Ellipses 1 is the most similar in eccentricity to the Earth's orbit
HELP PLEASEEEEEEEEEEEWE
Answer:
Answers are in the image
Step-by-step explanation:
Hope I got everything right and hope that helps you
