A rectangle has a perimeter of 42 ft its length, L, is 3 feet more than twice its width, W.
(c) Solve the system of equations that you just created by substitution to find the values of the length and width.
Answer:
Length of rectangle = 15 feet
Width of rectangle = 6 feet
Step-by-step explanation:
Given:
Perimeter of rectangle = 42 ft
Length of rectangle = 2[Width of rectangle] + 3
Find:
Value of length and width
Assume:
Width of rectangle = w
SO,
Length of rectangle = 2[w] + 3
Perimeter of rectangle = 2[l + b]
42 = 2[2w + 3 + w]
2[3w + 3] = 42
6w + 6 = 42
6w = 42 - 6
6w = 36
w = 36 / 6
w = 6
So,
Width of rectangle = 6 feet
Length of rectangle = 2[w] + 3
Length of rectangle = 2[6] + 3
Length of rectangle = 12 + 3
Length of rectangle = 15 feet
A chi-square test was conducted to investigate whether there is an association between a person's favorite flavor of ice cream and their favorite toppings. Each of 200 randomly selected customers at an ice cream parlor was asked to pick their favorite flavor from vanilla, chocolate, chocolate chip, or none of these. They were also asked to pick their favorite topping from chocolate sauce, peanuts, crumbled cookies, crushed candies, or none of these. The hypothesis test had a test statistic of 24.97 with an associated p-value of 0.015. If the significance level of the test was a = 0.05, which of the following is the correct decision for this hypothesis test?
A. There is not convincing statistical evidence to suggest an association between favorite ice cream flavor and favorite topping.
B. There is convincing statistical evidence to suggest an association between favorite ice cream flavor and favorite topping.
C. There is convincing statistical evidence to suggest there is not an association between favorite ice cream flavor and favorite topping.
D. There is proof that a person's favorite ice cream topping is dependent on the person's favorite ice cream flavor.
E. There is proof that a person's favorite ice cream topping is independent of the person's favorite ice cream flavor.
Answer:
B
Step-by-step explanation:
I hope it is correct :)
Answer:
The answer is definitely B
Step-by-step explanation:
I just did this question on my test.
An insect population triples every 4 months. If the population started out with 24 insects, how many
insects would there be in 16 months?
Answer:
After 16 months there will be a population of 1,944 insects.
Step-by-step explanation:
Since an insect population triples every 4 months, if the population started out with 24 insects, to determine how many insects would there be in 16 months, the following calculation must be performed:
X = 24 x 3 ^ (16/4)
X = 24 x 3 ^ 4
X = 1,944
Thus, after 16 months there will be a population of 1,944 insects.
Complete the sentence.
9 is 36% of ??
Answer:
25
Step-by-step explanation:
Ratios:
[tex]\frac{36}{100} =\frac{9}{x} \\\\36x=900\\x=25[/tex]
Double check:
25(0.36) = 9
What are the ordered pairs of the
solutions for this system of equations?
f(x) = x2 – 2x + 3; f(x) = –6x
(-3, [?]); ([ ]), ([ ])
Answer:
[tex] {x}^{2} - 2x + 3 = - 6x \\ = {x}^{2} - 2x + 6x + 3 = 0 \\ \\ = {x}^{2} + 4x + 3 = 0 \\ = (x + 1)(x + 3) \\ = x = - 1and \: x = - 3[/tex]
Help please will mark brainliest!!!
Answer:
18
Step-by-step explanation:
What is the arc measure of major arc \stackrel{\large{\frown}}{ACB}
ACB
⌢
A, C, B, start superscript, \frown, end superscript on circle PPP in degrees?
Answer:
286°
Step-by-step explanation:
A circle is the locus of a point such that its distance from a fixed point (known as the center) is always constant. This distance is known as the radius of the circle.
A major arc is an arc larger than a semicircle, therefore its measure is greater than 180°. A minor arc is an arc smaller than a semicircle, therefore its measure is less than 180°.
The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=angle\ about\ a\ point-\stackrel{\large{\frown}}{AB}[/tex]
The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=360-74=286^o\\[/tex]
Leanna opens a savings account with an initial balance of $100. She then deposits $50 each month. Use an equation, a table, and a graph to explain the relationship between the amount of money in the account, a, and the number of months since Leanna opened the account, m.
Part A Write an equation to represent the problem. Explain how the value of a changes as m increases.
Part B Make a table to show the relationship between m and a. Find 5 ordered pairs.
Part C Use your table from Part B to draw a graph to represent the situation.
Please answer all questions
See the attached picture:
help me find the answers please
Answer:
x = 6.25
Step-by-step explanation:
Suppose y = 2x - 2.5. Find x when y = 10
this gives us the equation:
10 = 2x - 2.5
add 2.5 to both sides
2x = 12.5
divide both sides by 2
x = 6.25
Please LMK if you have questions.
1/2 minus 2/3
I have trouble with fractions
Answer:
-1/6
Step-by-step explanation:
Hope this helps down below! Pls mark brainliest
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(12×33)−(23×22)=?
Complete the multiplication and the equation becomes
36−46=?
The two fractions now have like denominators so you can subtract the numerators.
Then:
3−46=−16
This fraction cannot be reduced.
Therefore:
12−23=−16
Solution by Formulas
Apply the fractions formula for subtraction, to
12−23
and solve
(1×3)−(2×2)2×3
=3−46
=−16
Therefore:
12−23=−16
Real word example where a
piecework function might be used
9514 1404 393
Explanation:
Garment factory: workers may get paid by the number of pieces they complete.
__
Wood chopping: the worker gets paid by the number of cords of wood they produce, not by how long it takes.
__
Haircut -- the cost is the same (for the same type haircut) even if more time is spent
____
The above are instances where an individual worker gets paid by the piece they produce. There are numerous instances of companies getting paid by the job, regardless of the length of time or the quantity of materials required to do the job.
Lawn mowing -- the price is fixed each time the crew mows the lawn
Oil Change -- the cost of changing the oil in the car is not dependent on the time it takes or the amount of oil used
Car wash -- a fixed price is paid each time (at an automatic car wash)
Side A=3 cm
Side B=?
Side C( Hypotenuse)=6 cm
Find missing side of right triagle using Pythagorean Theorem
a
3 cm
3 square root (5) cm
3square root (3) cm
6 cm
Answer:
3sqrt3 cm
Step-by-step explanation:
6^2-3^2
36-9=27
sqrt27 = 3sqrt3
Answer:
c. 3 square root ( 3 ) cm
Step-by-step explanation:
C^2 = A^2 + B^2
A^2 = C^2 - B^2
= 6^2 - 3^2
= 36 - 9
A^2 = 27
A = 3√3 cm
Simplify: (3^5)^2 / 3^-2
A) 3^10
B) 3^9
C) 3^12
D) 3^8
Answer:
3^12
Step-by-step explanation:
(3^5)^2 / 3 − ^2 = 243^2/3−^2 = 59049 / 3−^2 = 59049/ 1 / 9 = 531441
= 3*3*3*3*3*3*3*3*3*3*3*3 = 3^12
Please answer please
9514 1404 393
Answer:
3629.84 cm²
Step-by-step explanation:
Put the given numbers into the area formula and do the arithmetic.
The area of a sphere is given by ...
A = 4πr²
A = 4(3.14)(17 cm)² = 3629.84 cm²
The ball has a surface area of about 3629.84 cm².
Grandma received 0.25 liters of medicine from her doctor. The directions asked her to take one teaspoonful 3 times daily until it is finished. A full teaspoon has a capacity of 4 ml. Grandma started taking her medicine on November 20th. What date should the medicine finish?
Answer:
Dec 10
Step-by-step explanation:
0.25 liter = 250 ml
4 ml * 3 = 12 ml
250/12 = 20.83 days
Nov 20 - Nov 30: 11 days
Dec 1 - Dec 9: 9 days
On December 9, she can still take her 3 doses.
By December 9, she will have taken 12 ml per day for 20 days for a total of 240 ml. She has 10 ml left for Dec 10th.
On Dec 10, she will take 2 doses of 4 ml and 1 dose of 2 ml, and she will finish the medicine.
sorry for the bad picture. I’m confused on how to solve this as it feels like I don’t have all the information needed.
i am so confused. not sure how to solve need step by step instruction to help please
given:f(x)=3x−7 for × ≥0
f(x)=-2x +3 for x >0
find: f(-5)
Answer:
13
Step-by-step explanation:
Since -5 is less than zero, we use the second equation, and substitute the -5 in for the x.
-2(-5)+3=13
Find a formula for the exponential function passing through the points
4
3,
and (1,20)
125
f(x) -
Answer:
[tex]y = 4*5^x[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]
[tex](x_2,y_2) = (1,20)[/tex]
Required
Determine the exponential equation
An exponential equation is of the form: [tex]y = ab^x[/tex]
In: [tex](x_2,y_2) = (1,20)[/tex]
[tex]20 = ab^1[/tex]
[tex]20 = ab[/tex] ---- (1)
In: [tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]
[tex]\frac{4}{125} = ab^{-3}[/tex] --- (2)
Divide (1) by (2)
[tex]20/\frac{4}{125} = \frac{ab}{ab^{-3}}[/tex]
[tex]20/\frac{4}{125} = b^4[/tex]
[tex]20*\frac{125}{4} = b^4[/tex]
[tex]5*125 = b^4[/tex]
[tex]625 = b^4[/tex]
Take 4th roots of both sides
[tex]\sqrt[4]{625} = b[/tex]
[tex]5 = b[/tex]
[tex]b = 5[/tex]
Substitute [tex]b = 5[/tex] in [tex]20 = ab[/tex]
[tex]20 = a * 5[/tex]
Solve for a
[tex]a = 20/5[/tex]
[tex]a = 4[/tex]
Hence, the equation is:
[tex]y = 4*5^x[/tex]
Find the average number of people in these cities: New York, Philadelphia, Chicago and Detroit a. 3.35 million b. 40 million. C. 4.0 million d. 33.million
Answer:
The answer is maybe going to be D which is 33 million
Step-by-step explanation:
New york is a big city
The diameter of the colosseum is about 167 meters. Therefore the circumference of the colosseum is
Answer:
C≈524.65m
Solving for C
C=πd=π·167≈524.64597m
Roller skates that usually sells for $125 is on sale for 35% off. Find the sale price.
Answer:
$81.25
Step-by-step explanation:
First find 35% of 125 which is 43.75
Next subtract 43.75 from 125
Your answer is $81.25
Replacing only the minimum value in a data to a smaller number will also change the mean
A.always
B. Sometimes
C.never true
What is the unit price of a granola bar if 8 granola bars cost $4.16
Answer:
divide 8 by 4.16
Step-by-step explanation:
Answer:
52 cents
Step-by-step explanation:
what is the distance between x=-2 and x=10
Answer:
12 prob
Step-by-step explanation:
which is the largest interval over which the function shown in the table is increasing?
x y=-- x2 ?
-4
-8
-
-2
-2
(x, y)
(-4,-8)
(-2,-2)
(0,0)
(2.-2)
(4.-8)
0
NO
-2
4
-8
O
A. x < -2
O B. x<0
C. X>0
D. X> 2
Answer:
x < 0
Step-by-step explanation:
If you were to graph the function, you would get a parabola that opens down with the vertex at (0, 0). So, the graph is increasing from -∞ to 0.
m
Find the measure of the angles.
Answer:
where is your figure please send it
Select the figure that is not a net for a cube. Complete the explanation.
When the figure is folded, _____
of the faces will overlap.
He measured the pool’s dimensions to be 15 feet long by 35 feet wide. The actual dimensions of the pool are 14.5 feet by 34.75 feet. Find Jack’s percent error to the nearest percent.
Answer:
Percent error = -4.02 (Approx.)
Step-by-step explanation:
Given:
Estimated pool dimension = 15 ft long and 35 ft wide
Actual pool dimension = 14.5 ft long and 34.75 ft wide
Find:
Percent error
Computation:
Area of Estimated pool = 15 x 35
Area of Estimated pool = 525 ft²
Area of Actual pool = 14.5 x 34.75
Area of Actual pool = 508.875 ft²
Percent error = [(Actual - Estimated) / Estimated]100
Percent error = [(508.875 - 525) / 525]100
Percent error = [(-21.125) / 525]100
Percent error = -4.02 (Approx.)
The first step in determining the solution to the system of equations, y = –x2 – 4x – 3 and y = 2x + 5, algebraically is to set the two equations equal as –x2 – 4x – 3 = 2x + 5. What is the next step?
Set y = 0 in y = –x2 – 4x – 3.
Factor each side of the equation.
Use substitution to create a one-variable equation.
Combine like terms onto one side of the equation.
Answer:
Last one. Combine like terms onto side of the equation.
Step-by-step explanation:
The first step in determining the solution to the system of equations, [tex]y = -x^2 - 4x - 3[/tex] and [tex]y = 2x + 5[/tex] , algebraically is to set the two equations equal as [tex](-x^2 - 4x - 3) = 2x + 5[/tex], will be to set the equations equal to each other.
What is system of equations ?System of equations comprises of two or more equations of two or more variables and seeks common solutions to the equations.
We have,
[tex]y = -x^2 - 4x - 3[/tex]
[tex]y = 2x + 5[/tex]
So, to determine solution to these System of equations,
We have to
Set the equations equal to each other and solve for the value of [tex]x[/tex],
i.e.
[tex]-x^2 - 4x - 3=2x+5[/tex]
[tex]-x^2-6x-8=0[/tex]
[tex]x^2+6x+8=0[/tex]
[tex]x^2+4x+2x+8=0[/tex]
[tex]x(x+4)+2(x+4)=0[/tex]
[tex](x+2)(x+4)=0[/tex]
⇒ [tex]x+2=0[/tex]
[tex]x=-2[/tex]
[tex]x+4=0[/tex]
[tex]x=-4[/tex]
So, from the above solution we came to know that the first step in determining the solution to the given System of equations is to set the equations equal to each other.
To know more about System of equations click here
https://brainly.com/question/13760328
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Write an expression showing 5 less than the number K
Answer:
K-5
Step-by-step explanation:
Five less than K would be K-5.