Answer:
n = 8.5
Step-by-step explanation:
[tex]\frac{10}{n}[/tex] = [tex]\frac{2}{1.7}[/tex] ( cross- multiply )
2n = 10 × 1.7 = 17 ( divide both sides by 2 )
n = 8.5
At birth, one puppy weighs 15/16 pounds. A second puppy weighs 1 and 1/8 pounds. How much more did the second puppy weigh?
Answer:
3/16 pounds more.
Step-by-step explanation:
It is 1 1/8 - 15/16
= 9/8 - 15/16
= 18/16 - 15/16
= 3/16.
An entomologist can model the number of mosquitos in a forest as a function of
rainfall. In a similar way, they can also model the number of bats in the forest.
The function f(x) = 5x
22
gives the number of mosquitos in the forest (in
millions), and the function g(x) = 3a 0.5a² gives the number of bats (in millions
-
In both equations z represents rainfall (in centimeters). Here are the graphs of f and
G
The interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2
How to interpret the points of intersection?The graph of the two functions alongside their equations are the given parameters of this question
The functions are given as:
f(x) = 5x - x^2
g(x) = 3x - 0.5x^2
When the graphs of two curves or lines intersect on a coordinate plane, it means that the point of intersection represents where the graphs have equal value
In this case, it represents
f(x) = g(x)
Substitute the known values in the above equation
5x - x^2 = 3x - 0.5x^2
So, the interpretation of the point of intersection of the curves is (c) they give a solution to the equation 5x - x^2 = 3x - 0.5x^2
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Please help me i don’t understand
The graph of the inverse of the function is shown in the image attached below.
How to graph the inverse of a function
In this question we must apply the following transformation rule to the three points to determine the points of the inverse function:
(x, y) → (y, x)
Now we proceed to find the points:
(- 7, 3) → (3, - 7)
(-3, 0) → (0, -3)
(-2, -2) → (-2, -2)
Lastly, we proceed to construct the graph of the inverse of the function.
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Juan bought a sweater for $15.95 and two shirts for $9.00 each. how much did juan spend on clothes?
Answer:
Step-by-step explanation:
Well first you have:
$15.95 for one sweater
$9.00 each for two shirts
You would double the amount $9.00 which would be:
9 + 9 = 18 or Multiply 9 x 2 = 18
So this would total to 15 + 18 = $33
In a sample of 16 employees randomly selected at a company, the average age is 25 years and the standard deviation is 2 years. We want to test if the average age of all employees is greater than 24. If ages are normally distributed in the population, using a significance level of 0.05, we can claim that the population mean is: Group of answer choices
If ages are normally distributed then using a significance level of 0.05 , we can claim that the population mean is greater than 24.
Given sample mean of 25 years , sample size of 16 ,standard deviation of 2 years.
We have to find whether the population average is greater than 24.
We have to use t test because n is less than 30. It is right tailed.
We have to first form Hypothesis.
[tex]H_{0}[/tex]:μ>24,
[tex]H_{1}[/tex]:μ<24.
t=X-μ/S/[tex]\sqrt{n}[/tex]
t critical at 5% significance level and degree of freedom=15 (16-1)=1.7531
t=24-25/2/[tex]\sqrt{16}[/tex]
=-1/0.5
=-2
Because 1.7531 is greater than -2 so we will accept the null hypothesis.
Hence we can say that the average of population is greater than 24.
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Can someone help? ASAP
Answer:
11. [tex]\frac{\sqrt{2} }{2}[/tex]
12. [tex]\sqrt{3}[/tex]
13. [tex]\frac{\sqrt{3} }{2}[/tex]
14. [tex]\frac{\sqrt{3} }{3}[/tex]
15. [tex]\sqrt{2}[/tex]
16. [tex]\frac{2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
Hope this helps
Multiply the following numbers. Reduce the answer to lowest terms.
Answer:
B 4 1/3
Step-by-step explanation:
Triangle X Y Z is shown. Angle X Z Y is 90 degrees and angle X Y Z is 41 degrees. The length of Z X is 22.
Which equation could be used to solve for the length of XY?
XY = (22)sin(41°)
XY = (22)cos(41°)
XY = StartFraction 22 Over cosine (41 degrees) EndFraction
XY = StartFraction 22 Over sine (41 degrees) EndFraction
The equation that could be used to solve for the length of XY is XY = 22/sin(41)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Sine rule is used to show the relationship between the sides and angles of a trinagles.
Using sine rule on triangle XYZ:
XY / sin(Z) = XZ / sin(Y)
XY / sin(90) = 22/sin(41)
XY = 22/sin(41)
The equation that could be used to solve for the length of XY is XY = 22/sin(41)
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Answer:
D
Step-by-step explanation:
given that f.x 3x-2 over x+1 g[x] x +5 evaluate f[-4] and gf [-2]
The value of f[ -4 ] and g°f[-2] are [tex]\frac{14}{3}[/tex] and 13 respectively.
What is the value of f[-4] and g°f[-2]?Given the function;
[tex]f(x) = \frac{3x-2}{x+1}[/tex][tex]g(x)=x+5[/tex]f[ -4 ] = ?g°f[ -2 ] = ?For f[ -4 ], we substitute -4 for every variable x in the function.
[tex]f(x) = \frac{3x-2}{x+1}\\\\f(-4) = \frac{3(-4)-2}{(-4)+1}\\\\f(-4) = \frac{-12-2}{-4+1}\\\\f(-4) = \frac{-14}{-3}\\\\f(-4) = \frac{14}{3}[/tex]
For g°f[-2]
g°f[-2] is expressed as g(f(-2))
[tex]g(\frac{3x-2}{x+1}) = (\frac{3x-2}{x+1}) + 5\\\\g(\frac{3x-2}{x+1}) = \frac{3x-2}{x+1} + \frac{5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) = \frac{3x-2+5(x+1)}{x+1}\\\\g(\frac{3x-2}{x+1}) = \frac{8x+3}{x+1}\\\\We\ substitute \ in \ [-2] \\\\g(\frac{3x-2}{x+1}) = \frac{8(-2)+3}{(-2)+1}\\\\g(\frac{3x-2}{x+1}) = \frac{-16+3}{-2+1}\\\\g(\frac{3x-2}{x+1}) = \frac{-13}{-1}\\\\g(\frac{3x-2}{x+1}) = 13[/tex]
Therefore, the value of f[ -4 ] and g°f[-2] are [tex]\frac{14}{3}[/tex] and 13 respectively.
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Mr. lee walks into the courtyard after school and wants to know the height of the tree. he measures an angle of 47* between a line of sight to the top of the tree and the ground and he is 22 feet away from the tree. how tall is the tree? *
The tree is 23.54 feet tall.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean.
According to the question,
Height of tree= 22*tan [tex]47^{o}[/tex]
= 22* 1.07
= 23.54 ft.
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Raj measures the height of 70 plants calculate the estimate of the mean height of the plants
The mean height of plants is 44.07cm.
Given that a raj measures the height of 70 plants which is shown in the table in the image attached below.
The mean is defined as the mean value equal to the ratio of the total number of a given set of values to the total number of values contained in that set.
Firstly, we will find the midpoint of the height by using the formula
(upper limit +lower limit)/2
When h is 10<h<20 then the midpoint is
x₁=(10+20)/2
x₁=15
When h is 20<h<0 then the midpoint is
x₂=(20+40)/2
x₂=30
When h is 40<h<50 then the midpoint is
x₃(40+50)/2
x₃=45
When h is 50<h<60 then the midpoint is
x₄=(50+60)/2
x₄=55
When h is 60<h<90 then the midpoint is
x₅=(60+90)/2
x₅=75
Now, we will find the mean height by using the formula
x=(f₁x₁+f₂x₂+f₃x₃+f₄x₄+f₅x₅)/(Σfi)
Here, f₁=7,f₂=15,f₃=27,f₄=13,f₅=8
and Σfi=7+15+27+12+8=70
Substitute these values in the formula, we get
x=(7×15+15×30+27×45+12×55+8×75)/70
x=(105+450+1215+715+600)/70
x=(3085)/70
x=44.07
Hence, the estimate of the mean height of the plants when raj measures the height of 70 plants is 44.07cm.
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Explain or show how to determine if the following coordinates are a solution to the following system of linear inequalities. y<4x+8 y>x-6
The inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
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How do I solve this problem 34=p+19
Hello,
[tex]34 = p + 19[/tex]
[tex]34 - 19 = p + 19 - 19[/tex]
[tex]15 = p[/tex]
[tex]p = 15[/tex]
For the graph x = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is undefined and the slope of the perpendicular line is 0
How to determine the slope?The equation is given as:
x = 1
The above do not have any y value.
This means that the slope of the line is undefined
i.e.
m = undefined
The slope of the parallel line is:
Slope = m
This gives
Slope = undefined
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/undefined
Slope = 0
Hence, the slope of the parallel line is undefined and the slope of the perpendicular line is 0
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In London, the charge of a tour bus consists of a fixed rental price plus a per kilometre rate, that depends on the distance of the trip.
The per kilometre rate is $12/km. You decide to go on a 5 km trip, and it costs you $70.
a) What is the fixed rental cost? Show your work.
b) Determine the equation relating the cost, C, in dollars, and the distance, d, in km.
d) What is the cost of an 18 km trip?
e) What is the distance travelled if the total cost is $250?
PLEASEEEEEEEE
Using a linear function, we have that:
a) The fixed cost is of $10.
b) The equation is: C = 10 + 12d.
c) The cost of an 18 km trip is $226.
d) The distance traveled is of 20 km.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the slope is of m = 12. When d = 5, C(d) = 70, hence we find the fixed cost as follows:
C(d) = 12d + b
70 = 60 + b
b = 10.
Hence the equation is:
C(d) = 12d + 10.
For a trip of 18 km, d = 18, hence the cost is:
C(12) = 12 x 18 + 10 = $226.
When the cost is of $250, the distance is found as follows:
250 = 12d + 10
12d = 240
d = 240/12
d = 20 km.
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How many different 4 digit numbers can be formed using only digits 1,2,3 and 4 given that they contain each of these digits as many times as you want?
The number of different 4 digit numbers that can be formed using only digits 1,2,3 and 4 if they are repeated is; 256 possible numbers
How to find the probability combination?Since the numbers can be used as many times as we want, then it means they can be repeated.
Thus, if we are looking at the number of 4 digit numbers we can create using the numbers 1, 2, 3, and 4, we can calculate that the following way:
For each digit (thousands, hundreds, tens, ones), we have 4 possible choices of numbers. And so we can create;
4 × 4 × 4 × 4 = 256 numbers
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Which of the following parabolas has its vertex the furthest away from the x-axis
Oy
x² - 1
y = 3x² + 4
Oy
=
Y =
1/2x²
Oy = x² - 10
Question 12 (1 point)
Answer:
y=x^2-10
Step-by-step explanation:
what is 12(w-3) if w= 10
Hey there!
12(w - 3)
= 12(10 - 3)
= 12(10) + 12(-3)
= 120 - 36
= 84
OR
12(w - 3)
= 12(10 - 3)
= 12(7)
= 84
Therefore, your answer should be:
84
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
How many quarters are there in 7 1/2?
Answer: 30.
Step-by-step explanation:
[tex]7\frac{1}{2} =\frac{7*2+1}{2} \\\frac{14+1}{2}=\frac{15}{2}\\ \frac{15*2}{2*2}=\frac{30}{4} \\ \frac{30}{4}=30*\frac{1}{4} .[/tex]
There are total 30 quarters in [tex]7\frac{1}{2}[/tex].
What is one quarter?A quarter is one out of four equal parts. One quarter is the same as the fraction ¼.
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction.
How to convert a mixed fraction into an improper fraction?To change a mixed fraction to an improper fraction, we multiply the whole number by the denominator and then add this product with the numerator.
According to the given question.
We have a mixed fraction [tex]7\frac{1}{2}[/tex].
So, the improper fraction of the given mixed fraction is given by
[tex]7 \frac{1}{2} = \frac{15}{2}[/tex]
To find the number of quarters in the given mixed fraction, we will divide [tex]7\frac{1}{2}[/tex] by [tex]\frac{1}{4}[/tex].
Therefore,
[tex]\frac{7\frac{1}{2} }{\frac{1}{4} }[/tex]
= [tex]\frac{\frac{15}{2} }{\frac{1}{4} }[/tex]
[tex]= \frac{15\times 4}{2}[/tex]
[tex]= 15\times 2[/tex]
[tex]= 30[/tex]
Hence, there are total 30 quarters in [tex]7\frac{1}{2}[/tex].
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Which function could be a stretch of the exponential decay function shown on the graph?
f(x) = 2(6)x
f(x) = One-half(6)x
f(x) = 2(one-sixth) Superscript x
f(x) = One-half (one-sixth) Superscript x
The function that could be a stretch of the exponential decay function shown on the graph is B. f(x) = One-half(6)x.
How to illustrate the function?From the information given, it can be seen that function A is a monotonically increasing function.
Also, it can be seen that C and D don't pass through (0, 1).
Therefore, the function could be a stretch of the exponential decay function shown on the graph is B.
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Answer:
b
Step-by-step explanation:
What is the slope of the line through (-1,8)(−1,8)left parenthesis, minus, 1, comma, 8, right parenthesis and (3,-4)(3,−4)left parenthesis, 3, comma, minus, 4, right parenthesis? Choose 1 answer: Choose 1 answer: (Choice A) A \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction (Choice B) B 333 (Choice C) C -\dfrac13− 3 1 minus, start fraction, 1, divided by, 3, end fraction (Choice D) D -3−3
The slope of the line through the points is -3
How to determine the slope?The points are given as:
(-1, 8) and (3, -4)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (-4 - 8)/(3 + 1)
Evaluate the expression
m = -3
Hence, the slope of the line through the points is -3
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The slope of the line that passes through (-1, 8) and (3, -4) is: -3.
How to Find the Slope of a Line?Slope of a line (m) = change in y / change in x.
Given the points, (-1, 8) and (3, -4):
Slope (m) = (-4 - 8)/(3 - (-1))
Slope (m) = (-12)/(4)
Slope (m) = -3
Thus, the slope that passes through the given points is: -3.
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Find the fifth term of the sequence.
a) Substituting in n = 2,
[tex]\frac{3(2)^{2}}{2}=6[/tex]
b) Substituting in n = 5,
[tex]\frac{3(5)^{2}}{2}=\frac{75}{2}[/tex]
c) Setting the nth term to be greater than 50,
[tex]\frac{3n^{2}}{2}>50 \\ \\ n^{2} >\frac{100}{3} \\ \\ n>\frac{10}{\sqrt{3}} \\ \\ \lceil n \rceil = 6[/tex]
Direct materials $ 5.50 direct labor $ 3.00 variable manufacturing overhead $ 1.50 fixed manufacturing overhead $ 4.00 fixed selling expense $ 2.50 fixed administrative expense $ 2.00 sales commissions $ 1.00 variable administrative expense $ 0.50 13. if the selling price is $21.50 per unit, what is the contribution margin per unit? (do not round intermediate calculations. round your answer to 2 decimal places.)
The contribution margin per unit is $ 1.50
The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.
One of the main components of break-even analysis is the idea of contribution margin.
Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.
According to the question,
Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)
= $ 20
Selling Price per unit = $ 21.50
Thus, contribution margin per unit = $ (21.50 - 20)
= $ 1.50
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3x-6=15 what is the value of x?
Answer:
7
Step-by-step explanation:
frist simplfying
3x-6=15
addind six to both side
3x-6+6=15+6
3x=21 dividing by 3
x=7
It takes you two and a half hours to drive 175 miles. how fast were you driving? (mph)
If one travels 175 miles in 2hour 30 mins then his speed is 70 mph .
Calculation of the speedDistance travels= 175 miles
time is taken to cover 175 miles = 2.5 hours
We have to find out the speed in mph.
We know that,
Distance = speed x time
⇒speed = distance / time
Putting the value of distance and time, we get:
speed = 175 / 2.5 = 70 mph
Hence the final answer is 70 mph.
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Simplify:6 to the power of 5/6to the power of 2.
A.1/6 to the power of 3
B.6 ttpo 7
C.6ttpo 2
D.6ttpo 3
The value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
How to simplify the expression?The expression is given as:
6 to the power of 5/6to the power of 2.
Rewrite properly as:
6^5/6^2
Apply the law of indices
6^(5-2)
Evaluate the difference
6^3
Hence, the value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
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Brainliest for answer
A quadratic equation is graphed to the left. Which of the following equations could be paired with the graphed equation to create a system of equations whose solution set is comprised of the points (2,-4)and (-4,2)?
The linear function that goes through the points (2,-4) and (-4,2) is:
y = -x + 2.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A linear function going through the points (2,-4) and (-4,2) would intersect the parabola at these points, hence these points would be the solution for the system of equations.
The slope of the line is:
m = (-4 - 2)/(2 - (-4)) = -1.
The line goes through point (2,-4), that is, when x = 2, y = -4, which we use to find the y-intercept b.
y = -x + b
-4 = -2 + b
b = -2.
Hence the equation is:
y = -x + 2.
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The functions f(x) and g(x) are shown on the graph.
f(x) = log(x)
g(x)
6
Using fix), what is the equation that represents gix)?
A) g(x) = log5(x) - 3
B) g(x) = log5(x) + 3
C) g(x) = log5(x-3)
D) g(x) = log5(x+3)
Using translation concepts, the equation of g(x) is:
D) [tex]\log_5{x + 3}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, g(x) is a shift left of 3 units of [tex]f(x) = \log_5{x}[/tex], hence:
[tex]g(x) = f(x + 3) = \log_5{x + 3}[/tex], which means that option D is correct.
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URGENT, PLEASE ANSWER THESE QUESTIONS
Can send helicopter 3 but not helicopter 1 and 2.
What is distance formula?
Consider two points (x1, y1) and (x2, y2) in the two-dimension, then the distance between these two points is given by,
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
We will solve given problem as shown below:
Let fire have coordinate F (-3,-5)
Let Helicopter 1 have coordinate H1(1,4)
Let Helicopter 2 have coordinate H2(-2,3)
Let Helicopter 1 have coordinate H3(4, -2)
A. Distance between helicopter 1 and fire
[tex]=\sqrt{(1-(-3))^2+(4-(-5))^2}[/tex]
[tex]=\sqrt{16+81}[/tex]
[tex]=\sqrt{97}=9.8[/tex]
No, cannot send helicopter 1
B. Distance between helicopter 2 and fire
[tex]=\sqrt{(-3-(-2))^2+(-5-3)^2}[/tex]
[tex]=\sqrt{1+64}[/tex]
[tex]=\sqrt{65}=8.06[/tex]
No, cannot send helicopter 2
Distance between helicopter 3 and fire
[tex]=\sqrt{(4-(-3))^2+(-2-(-5))^2}[/tex]
[tex]=\sqrt{49+9}[/tex]
[tex]=\sqrt{58}=7.6[/tex]
Yes, can send helicopter 3
Hence, can send helicopter 3 but not helicopter 1 and 2.
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I really need help :(((
Answer:
B solving by factoringA the quadratic formulaStep-by-step explanation:
1.The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.
Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.
Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."
2.When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
This quadratic formula tells you the solutions based on the coefficients of the original equation, so does not require rearranging the equation in any way.