Answer:
Ic² + b²l = 13 units.
Step-by-step explanation:
We have to evaluate the expression Ic² + b²l with unknowns b and c and having the values of b and c respectively - 3 and - 2.
Now, Ic² + b²l
= I(- 2)² + (- 3)²l {Putting the values of b and c}
= I4 + 9l
= I13l
= 13 units.
Therefore, Ic² + b²l = 13 units. (Answer)
The perimeter of the rectangle is 76 units. Find the length of side pq
Answer: [tex]PQ=16\ units[/tex]
Step-by-step explanation:
The missing figure is attached.
The perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
Where "l" is the lenght and "w" is the width.
You can identify in the figure that:
[tex]w=SR=PQ=2z+2\\\\l=QR=PS=3z+1[/tex]
Then, knowing the perimeter of the rectangle, you can make the subsitution into the formula:
[tex]76=2(3z+1)+2(2z+2)[/tex]
Now you must simplify and solve for "z"
[tex]76=6z+2+4z+4\\\\76-6=10z\\\\70=10z\\\\\frac{70}{10}=z\\\\z=7[/tex]
Finally, substituting the value of "z" into [tex]PQ=2z+2[/tex], you get:
[tex]PQ=2(7)+2=16\ units[/tex]
team tool Bella canoed 15 3/4 miles in 5 1/4 hours
Answer:
Step-by-step explanation:
What's the question?
PICTURE BELOW Consider the net of a triangular prism where each unit on the coordinate plane represents four feet. If a sheet of plywood measures 4 ft x 8 ft, how many sheets of plywood will a carpenter need to build the prism?
A) 2
B) 3
C) 4
D) 5
Answer:
The carpenter will need 2 plywood to build the prism.
Step-by-step explanation:
Given:
The size of the plywood = 4 ft x 8 ft
1 Unit = 4 feet
To Find :
Number of plywood sheets the carpenter would need = "
Solution:
Step 1: Find the area of square
Area of the square is
=>[tex]4^2[/tex]
=>[tex]16 cm^2[/tex]
Here we have 3 square, so
[tex]3 \times 16[/tex]
=>[tex]48 ft^2[/tex]
Step 2 : Area of the triangle
Area of the triangle is
=>[tex]\frac{1}{2} \times b\times h[/tex]
=>[tex]\frac{1}{2} \times 4 \times 4[/tex]
=>[tex]\frac{16}{2} [/tex]
=>[tex]8ft^2[/tex]
[tex]2 \times 8 = 16ft^2[/tex]
Step 3: Finding the plywood needed
the total area of the triangular prism is
48 + 16= [tex]64 ft^2[/tex]
Area of the plywood wood is
=> [tex]4 \times 8[/tex]
=> [tex]32 ft^2[/tex]
Number of plywood required = [tex]\frac{\text {area of the prism}}{\text{area of one plywood}}[/tex]
=> [tex]\frac{64}{32}[/tex]
=> 2
Determine the coordinates of the corners of the rectangle to compute the perimeter of the rectangle using the distance formula (round to the nearest integer).
A) 17 units
B) 28 units
C) 30 units
D) 34 units
Answer:
D
Step-by-step explanation:
Line 1 thru (3,2) and (5,-1)
Answer:
The required equation of line is 3x + 2y =13
Step-by-step explanation:
Here we are given two points are we are supposed to find the line passing through the two points.
The given points are (3,2) and (5,-1).
There is only one line passing through these two points.
The slope of the given line = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
= [tex]\frac{-3}{2}[/tex]
y - [tex]y_{1} = m(x - x_{1})[/tex]
y - 2 = [tex]\frac{-3}{2}[/tex](x - 3)
2y - 4 = - 3x + 9
3x + 2y = 13
The required line is 3x + 2y = 13
A dairy farmer wants to mix a 85% protein supplement and a standard 55% protein ration to make 1200 pounds of a high-grade 80% protein ration. How many pounds of each should he use?
The diary farmer should use 1000 pounds of 85 % protien and 55 % of 200 pounds to make 1200 pounds of a high-grade 80% protein ration
Solution:
Let the amount of 85 % protien supplement be "x"
Then amount of 55 % protien be (1200 - x)
According to given question,
85 % of "x" protien supplement + 55 % of 1200 - x protien used to get 80 % of 1200 pounds
85 % of x + 55 % of (1200 - x) = 80 % of 1200
[tex]\frac{85}{100} \times x + \frac{55}{100} \times (1200 - x) = \frac{80}{100} \times 1200\\\\0.85x + 0.55(1200 - x) = 960\\\\0.85x + 660 - 0.55x = 960\\\\0.3x = 960 - 660\\\\0.3x = 300\\\\x = 1000[/tex]
Pounds of 85 % protien used = 1000 pounds
Then pounds of 55 % protien used = 1200 - 1000 = 200 pounds
Thus he should use 1000 pounds of 85 % protien and 200 pounds of 55 % protien to get 1200 pounds of a high-grade 80% protein ration
kayla is on level 12 of a new game. Every Day she completes 6 new levels. Maddy is on level 28 of the same game. Every Day she completes 2 new levels. When will they be on the same level? what level will that be?
We know that Kayla is level 12 and gains 6 levels everyday. We know that Maddy is level 28 and gains 2 levels everyday. To find which day they are both the same level we can add.
-------------------------
Day 1:
Kayla is level 12
Maddy is level 28
Day 2:
Kayla is level 18 (12 + 6)
Maddy is level 30 (28 + 2)
Day 3:
Kayla is level 24 (18 + 6)
Maddy is level 32 (30 + 2)
Day 4:
Kayla is level 30 (24 + 6)
Maddy is level 34 (32 + 2)
Day 5:
Kayla is level 36 (30 + 6)
Maddy is level 36 (34 + 2)
-------------------------
They willl be at the same level on level 36.
-------------------------
Best of luck!
Which of the following equations best describes a square root function that is reflected across the x-axis and has a vertex of (−4,2)?
A. [tex]y=\sqrt{-(x-4)} +2[/tex]
B. [tex]y= -\sqrt{x+2}-4[/tex]
C. [tex]y=-\sqrt{x+4} +2[/tex]
D. [tex]y=-\sqrt{x-4} +2[/tex]
Answer:
C
Step-by-step explanation:
Rather than picking, let's try to construct one from the description.
reflected over the x axis means -[tex]\sqrt{x}[/tex]
the vertex is usually at (0,0), now how do we move a graph? or in other words translating it.
To move left and right you use [tex]\sqrt{x-h}[/tex] where if you subtract h you move right and if you add h you move left. we go from (0,0) to (-4,2). so 0 to -4 is 4 left, so that means we add 4.
To move up and down we use [tex]\sqrt{x}+v[/tex] Here if v is positive you move up and if v is negative you move down. going from (0,0) to (-4,2) it moves up 2
So now we put them all together [tex]-\sqrt{x+4}+2[/tex] And if you look, C matches that exactly.
The correct equation is option C: y = -√(x + 4) + 2, which describes a square root function reflected across the x-axis with a vertex at (-4, 2).
We are given a square root function that is reflected across the x-axis and has a vertex at (-4, 2). Let's analyze which of the provided options fits this description step by step.
Starting with the reflection across the x-axis, the function must have a negative sign outside the square root. This eliminates option A.Next, we focus on the vertex. The general form of a square root function is y = a√(x - h) + k where (h, k) is the vertex of the graph. Here, the vertex is (-4, 2).This means our function should resemble y = -√(x + 4) + 2 because shifting x by +4 (making x + 4 = 0 when x = -4) moves the vertex to (-4, 2).Reviewing the options, purely C: y = -√(x + 4) + 2 fits this format.Thus, option C is the correct equation that describes the square root function reflected across the x-axis with a vertex at (-4, 2).
Find the measure of Angle X. x = 150˚ x = 120˚ x = 145˚ x = 90˚
Answer:
[tex]m\angle x=120^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle y
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the bottom triangle of the figure
[tex]30^o+30^o+m\angle y=180^o[/tex]
solve for y
[tex]60^o+m\angle y=180^o[/tex]
[tex]m\angle y=180^o-60^o[/tex]
[tex]m\angle y=120^o[/tex]
step 2
we know that
[tex]m\angle x=m\angle y[/tex] ----> by vertical angles
we have
[tex]m\angle y=120^o[/tex]
therefore
[tex]m\angle x=120^o[/tex]
Answer:
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of angle y
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the bottom triangle of the figure
solve for y
step 2
we know that
----> by vertical angles
we have
therefore
Step-by-step explanation:
3. Greg wants to save $1,500 in a year. Can he do this by having
$20 from each weekly paycheck deposited into a savings
account? Explain.
If Greg saves $20 per week from his paycheck, by the end of the year he would have saved $1,040, which is less than his goal of $1,500. Thus, he cannot reach his goal with this savings plan.
Explanation:The question asks if Greg can save $1,500 in a year by putting away $20 from his weekly paycheck into a savings account. If we multiply $20 (the amount he saves each week) by 52 (the number of weeks in a year), we get $1,040. So, Greg will have saved $1,040 in a year, which is less than his goal of $1,500. Therefore, saving $20 from each weekly paycheck will not allow Greg to reach his goal of $1,500 in a year.
Learn more about Savings Plan here:https://brainly.com/question/34205262
#SPJ3
If x/a = 4, a/y = 6, a2 = 9 and ab2 = −8 then x + 2y = ?
Select one:
A. −10
B. −15
C. −5
D. −13
Answer:
-13
Step-by-step explanation:
We are given:
[tex]\frac{x}{a}=4[/tex]
[tex]\frac{a}{y}=6[/tex]
[tex]a^2=9[/tex]
[tex]ab^2=-8[/tex]
Since [tex]ab^2=-8[/tex] then [tex]a[/tex] has to be negative.
Solving [tex]a^2=9[/tex] therefore gives [tex]a=-3[/tex].
(Note: [tex](-3)^2=(-3)(-3)=9[/tex].)
[tex]\frac{x}{a}=4[/tex] and [tex]a=-3[/tex] gives us:
[tex]\frac{x}{-3}=4[/tex].
Multiplying both sides by -3 gives: [tex]x=-12[/tex].
[tex]\frac{a}{y}=6[/tex] and [tex]a=-3[/tex] gives us:
[tex]\frac{-3}{y}=6[/tex].
Multiplying both sides by [tex]y[/tex] gives: [tex]-3=6y[/tex].
Divide both sides by 6 gives: [tex]\frac{-3}{6}=y[/tex].
Simplifying this gives us [tex]\frac{-1}{2}=y[/tex].
Now we are asked to find the numerical value for [tex]x+2y[/tex].
[tex]-12+2(\frac{-1}{2})[/tex]
[tex]-12+-1[/tex]
[tex]-13[/tex]
D.
What is the equation of a line that passes through the point (3,2) and has a slope of 1/3
Answer:
y-2=1/3(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-2=1/3(x-3)
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
100
,
80
,
64
,
.
.
.
100,80,64,...
Find the 9th term.
Find the
Answer:
The 9th term for given sequence is 16.777
Therefore the 9th term is [tex]a_{9}=16.777[/tex].
Step-by-step explanation:
Given first three terms of a sequence are 100,80,64,...
Given [tex]a_{1}=100[/tex] ,[tex]a_{2}=80[/tex] , [tex]a_{3}=64[/tex],...
Given sequence is of the form of Geometric sequence
Therefore it can be written as [tex]{\{a,ar,ar^2,...}\}[/tex]
therefore a=100 , ar=80 , [tex]ar^2=64[/tex] ,...
To find common ratio
[tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]r=\frac{80}{100}[/tex]
[tex]r=\frac{4}{5}[/tex]
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]r=\frac{64}{80}[/tex]
[tex]r=\frac{4}{5}[/tex]
Therefore [tex]r=\frac{4}{5}[/tex]
The nth term of the geometric sequence is
[tex]a_{n}=ar^{n-1}[/tex]
To find the 9th tem for the given geometric sequence is
[tex]a_{n}=ar^{n-1}[/tex]
put n=9, a=100 and [tex]r=\frac{4}{5}[/tex]
[tex]a_{9}=100(\frac{4}{5})^{9-1}[/tex]
[tex]=100(\frac{4}{5})^{8}[/tex]
[tex]=100(\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5})[/tex]
[tex]=100(\frac{256\times 256}{625\times 625})[/tex]
[tex]=100(\frac{65536}{390625})[/tex]
[tex]=100(0.16777})[/tex]
[tex]=16.777[/tex]
Therefore [tex]a_{9}=16.777[/tex]
The 9th term is 16.777
ms.jones tooke her family to the movies. there were a total of 12 people. children tickets cost $5 and adults tickets cost $10. she spent a total of $95. how maby children went to the movies
Answer:
5 children
Step-by-step explanation:
7 adults = $70
5 children = $25
total= 12 people
○○○○○○○○○○○○○○○
therefore 5 children went
○○○○○○○○○○○○○○○
Step-by-step nvm............
if the number of square centimetire on the surface of a sphear is equal to the number of cubic centimetres in its volume what is the diameter of the sphere
Answer:
The diameter of the sphere is 6 centimeters
Step-by-step explanation:
we know that
The surface area of a sphere is
[tex]SA=4\pi r^{2}[/tex]
The volume of the sphere is
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
Equate both formulas
[tex]\frac{4}{3}\pi r^{3}=4\pi r^{2}[/tex]
Simplify
[tex]\frac{1}{3}r^{3}=r^{2}[/tex]
[tex]\frac{r^3}{r^2}=3[/tex]
[tex]r=3\ cm[/tex]
Remember that the diameter is two times the radius
so
[tex]D=2r=2(3)=6\ cm[/tex]
therefore
The diameter of the sphere is 6 centimeters
Final answer:
The diameter of a sphere where the surface area equals the volume is 1.5 cm.
Explanation:
To find the diameter of a sphere where the surface area in square centimeters is equal to the volume in cubic centimeters, we use the formulae for the surface area and volume of a sphere:
Surface Area (SA) = 4πr²Volume (V) = 4/3πr³Since the surface area is equal to the volume (SA = V), we can set the equations equal to each other and solve for the radius (r):
4πr² = 4/3πr³r³/r² = 3/4r = 3/4Now that we have the radius, we can find the diameter, which is twice the radius:
Diameter (d) = 2r = 2 × (3/4) = 3/2 cm or 1.5 cm
What are the zeros of the following function?
y=x^2+x- 12
Answer:
-4, 3.
Step-by-step explanation:
x^2 + x - 12 = 0
(x + 4)(x - 3) = 0
x = -4, 3.
Please help I need to finish my winter packet and no one is answering my questions
Answer:
[tex]\sqrt[7]{x^{4}}[/tex]
[tex](x^{\frac{1}{7}})^{4}[/tex]
[tex](\sqrt[7]{x})^{4}[/tex]
Step-by-step explanation:
we have
[tex]x^{\frac{4}{7}}[/tex]
Remember the properties
[tex]\sqrt[n]{a^{m}}=a^{\frac{m}{n}}[/tex]
[tex](a^m)^{n}=a^{m*n}[/tex]
so
Verify each case
Part 1) we have
[tex]\sqrt[4]{x^{7}}[/tex]
we know that
[tex]\sqrt[4]{x^{7}}=x^{\frac{7}{4}}[/tex]
Compare with the given expression
[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]
Part 2) we have
[tex]\sqrt[7]{x^{4}}[/tex]
we know that
[tex]\sqrt[7]{x^{4}}=x^{\frac{4}{7}}[/tex]
Compare with the given expression
[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]
therefore
Is equivalent to the given expression
Part 3) we have
[tex](x^{\frac{1}{7}})^{4}[/tex]
we know that
[tex](x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]
Compare with the given expression
[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]
therefore
Is equivalent to the given expression
Part 4) we have
[tex](x^{\frac{1}{4}})^{7}[/tex]
we know that
[tex](x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]
Compare with the given expression
[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]
Part 5) we have
[tex](\sqrt[4]{x})^{7}[/tex]
we know that
[tex](\sqrt[4]{x})^{7}=(x^{\frac{1}{4}})^{7}=x^{\frac{7}{4}}[/tex]
Compare with the given expression
[tex]x^{\frac{7}{4}} \neq x^{\frac{4}{7}}[/tex]
Part 6) we have
[tex](\sqrt[7]{x})^{4}[/tex]
we know that
[tex](\sqrt[7]{x})^{4}=(x^{\frac{1}{7}})^{4}=x^{\frac{4}{7}}[/tex]
Compare with the given expression
[tex]x^{\frac{4}{7}} = x^{\frac{4}{7}}[/tex]
therefore
Is equivalent to the given expression
What is tan C ?
Figure shows right triangle A B C. Angle B is a right angle. Segment A B is 11 units. Segment B C is 22 units.
Express your answer as a simplified fraction.
Question 1 options:
1/2
1/4
1/3
2/1
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle ABC of the figure, the tangent of angle C is equal to divide the opposite side to angle C (side AB) by the adjacent side to angle C (side BC)
so
[tex]tan(C)=\frac{AB}{BC}[/tex]
substitute the given values
[tex]tan(C)=\frac{11}{22}[/tex]
simplify
[tex]tan(C)=\frac{1}{2}[/tex]
You put 1200 in an account that earns 3% simple interest. What is the total amount in the account after four years?
Answer: A = 1350.61
Step-by-step explanation:
Using the formula for calculating amount, which is given as
A = P [tex](1 + r)^{n}[/tex]
A = amount
P = Principal
r = rate
n = number of years
substituting the values given into the formula , we have
A = 1200 ([tex](1 + 0.03)^{4}[/tex]
A = 1200 ([tex](1.03)^{4}[/tex]
A = 1350.61
Therefore , the amount after four years is 1350.61
alex buys a car for $19,500 and later sells it at a profit of 20%.At what price did he sell the car?
Answer:
23400
Step-by-step explanation:
Answer:
$23,400
Step-by-step explanation:
19500*0.2=3900
19500+3900=23400
there are five boys and ten girls in mr johnsons gym class.the simplified ratio of boys to girls is 1/2. what does this ratio mean
Answer:
This ratio means for every boy there are two girls.
There are twice as many girls as there are boys. Backwards, it's there are half as many boys as there are girl.
The simplified ratio is found by reducing the ratio to the lower terms.
5/10 = 1/2
Both sides on the unsimplified ratio are division by 5. When done, it became 1/2.
According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. If a sample of 250 Colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in Colorado? A.6.75 B.7.82 C.10.33 D.11.97 E.61.17
Answer:
[tex]sd(X)=\sqrt{np(1-p)}=\sqrt{250*0.427*(1-0.427)}=7.82[/tex]
The best option is:
B.7.82
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Data given
[tex]p_C[/tex] represent the real population proportion for residents born in Colorado
[tex]\hat p_C =0.427[/tex] represent the estimated proportion for rsidents born in Colorado
[tex]n_C=250[/tex] is the sample size selected
Solution to the problem
Let X the random variable of interest (number of residents in the sample), on this case we now that:
[tex]X \sim Binom(n=250, p=0.427)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
The expected value is given by this formula:
[tex]E(X) = np=250*0.427=106.75[/tex]
And the standard deviation for the random variable is given by:
[tex]sd(X)=\sqrt{np(1-p)}=\sqrt{250*0.427*(1-0.427)}=7.82[/tex]
The best option is:
B.7.82
The standard deviation of the number of residents in the sample who were born in Colorado
B.7.82
hence option B is correct
Given
42.7 % of Colorado residents were born in Colorado.
If a sample of 250 Colorado residents is selected at random
We have to find out the standard deviation of the number of residents in the sample who were born in Colorado
The options are given below
A.6.75
B.7.82
C.10.33
D.11.97
E.61.17
This problem is given problem of binomial distribution is a discrete probability distribution of two independent events for the given parameters.
Number of Colorado students taken in sample = n = 250
Let, the percentage of Colorado residents that were born in Colorado be p
Let, the percentage of Colorado residents that were not born in Colorado be q
The percentage of Colorado residents that were born in Colorado = 42.7% = p = 0.427
[tex]\rm \m for \; a \; binomeal\; distribution \to p = 1-q ......(1)\\Equation \ (1)\; holds\; good[/tex]
So The percentage of Colorado residents that were not born in Colorado = q = (100-42.7) = 57.3 %
The standard deviation for binomial distribution is given by the formula as formulated in the equation number (1)
[tex]\rm \sigma = \sqrt{ n\times p\times q } .......(1)[/tex]
So we can write
Standard deviation of binomial distribution
[tex]\rm \sigma = \sqrt{ 250 \times \0.427 \times 0.573 } = 7.82[/tex]
The standard deviation of the number of residents in the sample who were born in Colorado
B.7.82
hence option B is correct
For more information please refer to the link below
https://brainly.com/question/15363285
What are the solutions to the equation (2x - 5)(3x – 1) = 0?
O x=-zor x=
O x=] or x=3
0
0
O
x = 5 or x = 1
Answer: x1=5/2
x2=1/3
Step-by-step explanation:
Eqation
(2x - 5)(3x – 1) = 0
has two options when 2x-5= 0 or 3x-1=0
2x-5=0
2x=5
X1=5/2
3x-1=0
3x=1
x2=1/3
jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit.
f(t)=2430(1.04)^28
a. rewrite the equation in the form f(t)=A(1+r/n)^nt
b. what is the annual interest rate?
Answer:
[tex]f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}[/tex]
The APR is 16%.
Step-by-step explanation:
Jason writes the following function to represent the amount of money in his account after 7 years given quarterly compounding of the $2430 initial deposit as
[tex]f(t) = 2430(1.04)^{28}[/tex] ......... (1)
a. If we want to rewrite the equation in the form
[tex]f(t) = A(1 + \frac{r}{n} )^{nt}[/tex] .......... (2)
Then comparing equation (1) and (2) we get, A = 2430 and t = 7
Hence, 7n = 28
⇒ n = 4
Now, [tex]1 + \frac{r}{4} = 1.04[/tex]
⇒ r = 0.16 i.e. 16%
Therefore, the expression is
[tex]f(t) = 2430(1 + \frac{0.16}{4} )^{7 \times 4}[/tex] (Answer)
b. The APR is 16%. (Answer)
Jackie is going to be the fastest woman in the world, Marion Jones. Marion can run 9.5m/s while Jackie can only run 7m/s. For obvious reasons, Jackie will get a headstart of 40m. How long should the race be so that Jackie barely wins?
Answer:
7x15+40=145
9.5x15=142.5
Step-by-step explanation:
To ensure Jackie barely wins the race with a 40m headstart against Marion, who runs at 9.5 m/s, we can calculate the distance of the race to be 112 meters, which Jackie will cover in 16 seconds at her speed of 7 m/s.
To determine how long the race should be so that Jackie barely wins over Marion Jones, we can utilize the concept of relative motion in physics. Given Marion's speed is 9.5 m/s and Jackie's speed is 7 m/s, and Jackie gets a 40m headstart, we can set up an equation to find the time it takes for Marion to catch up to Jackie.
We know the distance covered is speed times time, so for Marion: distance = 9.5 m/s time, and for Jackie: distance = 40m (headstart) + 7 m/s time. Since we are looking for the point where they are at the same distance we can set the equations equal to each other: 9.5 time = 40 + 7 time. Solving for time gives us:
9.5t = 40 + 7t
=> 2.5t = 40
=> t = 40 / 2.5
=> t = 16 seconds
Jackie will win the race if the race ends exactly when Marion catches up to her, so the race should be:
distance = 7m/s
16s = 112 meters
Therefore, the race needs to be 112 meters long for Jackie to barely win with a 40m headstart against Marion.
A furnace repair person charges an initial fee of $80 plus $30 per hour to do repairs.
a. After how many hours would the cost of the repair be at least $320?
b. How many hours did the repair person work if the total bill was $230?
Answer:
A) The repair bill would be at least $320 after 8 hours
B) The repairman would have worked for 5 hours
Step-by-step explanation:
A) Set up your equation with x equaling hours
30x + 80 = 320
subtract 80 to the opposite side of the equation
30x = 240
divide by 30
30x/30 = 240/30
x = 8
B) Set up your equation with x equaling hours
30x + 80 = 230
subtract 80 to the opposite side of the equation
30x = 150
divide by 30
30x/30 = 150/30
x = 5
After setting up inequalities for each scenario, we find that for the cost of the repair to be at least $320, at least 8 hours of work are required. When the total bill is $230, the repair person worked for 5 hours.
Explanation:To answer question (a) on how many hours the repair would need to be at least $320 given an initial fee of $80 and an hourly rate of $30, we set up the inequality:
80 + 30h ≥ 320
Subtract 80 from both sides to isolate the hourly term:
30h ≥ 240
Divide both sides by 30 to solve for h:
h ≥ 8
So, the repair would need to be at least 8 hours to cost $320.
To answer question (b) on how many hours the repair person worked for a total bill of $230, we use the equation:
80 + 30h = 230
Subtract 80 from both sides:
30h = 150
Divide both sides by 30:
h = 5
The repair person worked for 5 hours.
What is D and R? Please answer I need help.
Answer:
31. D: {8, 4, 0, -4}; R: {2, -1}; yes
32. D: {-1, 2, 7}; R: {-4, -3, -2, 0}; no
33. D: {-4, -3, -1, 2, 3, 5}; R: {-3, -2, 0, 3, 5}; yes
34. D: (-∞, ∞); R: (-∞, 4]; yes
35. D: [0, 5]; R: [-2, 3]; no
Step-by-step explanation:
In this context, D means "domain" and R means "range." The domain of a function is the list of input values for which the function is defined. For ordered pairs, it is the first number of the pair. For an x-y table, it is the list of x-values. For a graph, it is the possible values of x.
A relation is a function only if there are no repeated values in the domain (2 or more outputs for the same input.)
The range of a function is the list of output values produced by the function. For ordered pairs, it is the second number of the pair. For an x-y table, it is the list of y-values. For a graph, it is the possible values of y.
__
31. D: {8, 4, 0, -4}
R: {2, -1}
Function: yes
Domain and range values don't need to be repeated. Often, they're listed in order from lowest to highest. Here, we have listed them in order of occurrence in the function definition.
__
32. D: {-1, 2, 7}
R: {-4, -3, -2, 0}
Function: no
__
33. D: {-4, -3, -1, 2, 3, 5}
R: {-3, -2, 0, 3, 5}
Function: yes
__
34. D: (-∞, ∞)
R: (-∞, 4]
Function: yes
__
35. D: [0, 5]
R: [-2, 3]
Function: no . . . . . . there are 2 y-values for most x-values
The price of a scooter was rupees 34000 last year. It has increased by 20% this year. What is the price now?
Answer:
40,800Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\begin{array}{ccc}34,000&-&100\%\\\\x&-&20\%\end{array}\qquad\text{cross multiply}\\\\100x=(34,000)(20)\\\\100x=680,000\qquad\text{divide both sides by 100}\\\\x=\dfrac{680,000}{100}\\\\x=6,800\\\\34,000+6,800=40,800[/tex]
[tex]\bold{METHOD\ 2:}\\\\p\%=\dfrac{p}{100}\\\\\text{The price has increased by 20}\%\\\\100\%+20\%=120\%\\\\120\%=\dfrac{120}{100}=1.2\\\\120\%\ of\ 34,000\to1.2\cdot34,000=40,800[/tex]
Need answers ASAPP,please show work
This is the remainder when 64 oz is divided by 6 oz,
64 = 6 × 10 + 4
That's a remainder of 4.
Answer: 4 ounces
Answer:
Step-by-step explanation:
64 = 60 + 4 = 6*10 +4
Left over =4 ounce
Sharon will drink 4 ounces of juice
The ninth graders are hosting the next school dance. They would like to make at least a $500 profit from selling tickets. The ninth graders estimate that at most 300 students will attend the dance. They will earn $3 for each ticket purchased in advance and $4 for each ticket purchased at the door.
Answer:
I think you meant
Step-by-step explanation:
The ninth graders are hosting the next school dance. They would like to make at least a $500 profit from selling tickets. The ninth graders estimate that at most 300 students will attend the dance. They will earn $3 for each ticket purchased in advance and $4 for each ticket purchased at the door. Write a system of inequalities to represent this situation. Suppose only 30 people buy advance tickets. How many people would need to buy tickets at the door?