Explain why in a drawer containing only two different colors of socks one must draw only three socks to find a matching pair
Katy runs a day care center . So far this year , the enrollment has consisted of 2 toddlers and 8 children of other ages . Considering this data, how many of the next 20 children to enroll should you expect to be toddlers?
Answer:
You should expect 4 of the next 20 children to enroll to be toddlers.
Step-by-step explanation:
This question is solved by proportions.
So far:
We have that of 2 + 8 = 10 children, 2 are toddlers, so the proportion of toddlers is 2/10 = 0.2.
How many of the next 20 children to enroll should you expect to be toddlers?
0.2 out of 20, so: 0.2*20 = 4
You should expect 4 of the next 20 children to enroll to be toddlers.
A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these fish. Bass require 2 units of food A and 4 units of food B,
and trout require 5 units of food A and 2 units of food B. If the owner has 400 units of each food, find the maximum number of fish the lake can support.
fish
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Answer:
133 fishes
Step-by-step explanation:
Units of food A = 400 units
Units of food B = 400 units
Fish Bass required 2 units of A and 4 units of B.
Fish Trout requires 5 units of A and 2 units of B.
i. For food A,
total units of food A required = 2 + 5
= 7 units
number of bass and trout that would consume food A = 2 x [tex]\frac{400}{7}[/tex]
= 114.3
number of bass and trout that would consume food A = 114
ii. For food B,
total units of food B required = 4 + 2
= 6 units
number of bass and trout that would consume food B = 2 x [tex]\frac{400}{6}[/tex]
= 133.3
number of bass and trout that would consume food B = 133
Thus, the maximum number of fish that the lake can support is 133.
Solve the solution as an ordered pair
X + 9 = y
X = 4y - 6
Answer:
-10, -1
Step-by-step explanation:
See Image below:)
Choose which two numbers the following will fall between: *
V156 PLEASE HELP ME FASTTTTT
[tex]\sf\purple{A.\:Between \:12\:and\:13.}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \sqrt{156} \\ = 12.4899 \\ = 12.49[/tex]
Therefore, [tex] \sqrt{156} [/tex] will fall in between 12 and 13.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
the sumof 8pq and -17 pq is
Answer:
= -9pq
Step-by-step explanation:
=8pq + (-17pq)
=8pq-17pq
= -9pq
PLEASE ANSWER FAST
A-1 Equipment Rental Company charges $195 per day to rent a backhoe. The rental cost at A-1 can be represented by the function a(x) 195x, where x is the number of days the backhoe is rented. A competitor charges $150 per day plus an extra $90 fee. The cost at the competitor can be represented by the function c(x) 150x 90, where x is the number of days the backhoe is rented. Describe the transformation from the graph of a to the graph of c.
a. vertical shrink by 10/13 and then a vertical translation 90 units down
b. vertical stretch by 10/13and then a vertical translation 90 units up
c. horizontal stretch by 13/10and then a vertical translation 90 units up
d. vertical shrink by 10/13and then a vertical translation 90 units up
Answer:
cccccccccccccccccccc
This coordinate plane shows the journey of a plane between two cities. The journey starts from City A, indicated by a green point, and ends in City B, indicated by a red point. In which quadrant did the journey start and in what quadrant did it end?
A. Started in Quadrant III and ended in Quadrant I.
B. Started in Quadrant I and ended in Quadrant II.
C. Started in Quadrant II and ended in Quadrant IV.
D. Started in Quadrant I and ended in Quadrant III.
Answer:
Started in quadrant 2, ended in quadrant 4.
Step-by-step explanation:
The coordinate plane is divided into four quadrants. Quadrant one (QI) is the top right fourth of the coordinate plane, where there are only positive coordinates. Quadrant two (QII) is the top left fourth of the coordinate plane. Quadrant three (QIII) is the bottom left fourth. Quadrant four (QIV) is the bottom right fourth.
What is the equivalent recursive definition for an = 12+ (n - 1)3?
A. a1 = 3, An = An-1 + 12
B. a1 = 12, An = 30n-1
C. a1 = 12, Un = On-1 +3
D. a1 = n, an= 1201-1+3
Answer:
[tex]A_1 = 12[/tex]
[tex]A_n = A_{n-1} + 3[/tex]
Step-by-step explanation:
Given
[tex]A_n =12+(n-1)3[/tex]
Required
Write as recursive
We have:
[tex]A_n =12+(n-1)3[/tex]
Open bracket
[tex]A_n =12+3n-3[/tex]
[tex]A_n =12-3+3n[/tex]
[tex]A_n =9+3n[/tex]
Calculate few terms
[tex]A_1 =9+3*1 = 9 + 3 = 12[/tex]
[tex]A_2 =9+3*2 = 9 + 6 = 15[/tex]
[tex]A_3 =9+3*3 = 9 + 9 = 18[/tex]
The above shows that the rule is to add 3.
So, we have:
[tex]A_1 = 12[/tex]
[tex]A_n = A_{n-1} + 3[/tex]
Suppose you wanted to find a critical test statistic for a confidence interval for the slope of the regression line. How many degrees of freedom would you need to use?
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the regression line is not given.
However, I will give a general explanation of how to calculate the degree of freedom of a slope of regression line
The degree of freedom is calculated using:
[tex]df = n - k[/tex]
Where
[tex]k \to number\ of\ parameters[/tex]
[tex]n \to sample\ size.[/tex]
For a regression line; there are two parameters that are being estimates;
The intercept and the slope. So:
[tex]k = 2[/tex]
Hence, the degree of freedom of a slope of regression line is:
[tex]df = n -2[/tex]
So; if for example
[tex]n =101[/tex]
the degree of freedom will be:
[tex]df =101 - 2[/tex]
[tex]df =99[/tex]
An item was marked down 64% from its original price, x. The amount discounted was $30. Which equation can be
used to find the original price?
0.64(x) = 30
0.64(30) = x
30 +0.64 = x
x + 0.064 = 30
Answer:
0.64(x) = 30
Step-by-step explanation:
Hope that's correct.
3. The simple interest on $6,000 for 4 years is $1,680. *
NO LINKS!!!
What is the volume of this solid?
220 cubic units.
Answer:
Solution given:
for small cylinder
r=1
and for large cylinder
R=5+1=6
height for both [h]=2
Now
Volume of solid=πR²h-πr²h=πh(R²-r²)
=3.14*2(6²-1²)=219.8 =220 units ³.
Small cylinder is r=1
Large cylinder is R= 5+1 =6
Height (h) =2
Volume of solid,
→ πR²h-πr²h
→ πh(R²-r²)
→ 3.14 × 2(6²-1²)
→ 219.8
→ 220 cubic units
Answer the following.
A bag contains, 4, green balls 3 red balls, 6 yelow and 5 pink balls. A ball is
selected at random and not relased. The ball is green. What is the probably
of selecting another green be?
Express the answer as a frection |
Engress the answer as a decimal to three deomal places
ELess this answer as a percentage to the nearest Wacle number
Answer:
[tex]\frac{3}{17}, \\0.176, \\18\%[/tex]
Step-by-step explanation:
The area a total of 4+3+6+5=18 balls, consisting of:
4 green3 red6 yellow5 pinkAfter a green ball is selected (implied that it is not replaced or put back), there will be 17 balls total, consisting of:
3 green3 red6 yellow5 pinkTherefore, the probability of drawing another green one is:
[tex]\boxed{\frac{3}{17}=0.176=18\%}[/tex]
1 squared + 1= 2 sqaured - 2
2 sqaured + 2 = 3 squared - 3
3 squared + 3= 4 squared - 4
a) make a conjecture about this pattern. write your conjecture in words
b) generalise your conjecture for this pattern
c) prove that your conjecture is true
Answer:
It would be the letter B :)
Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 30 centimeters to 60 centimeters?
Answer:
The work done is 202.50Nm
Step-by-step explanation:
Given
[tex]F =450N[/tex]
[tex]x_1 = 30cm[/tex]
[tex]x_2 = 60cm[/tex]
Required
The work done
First, we calculate the spring constant (k)
[tex]F = kx_1[/tex]
[tex]450N = k *30cm[/tex]
[tex]k = \frac{450N}{30cm}[/tex]
[tex]k =15N/cm[/tex]
So:
[tex]F = kx_1[/tex]
[tex]F(x) = 15x[/tex]
The work done using Hooke's law is:
[tex]W =\int\limits^a_b {F(x)} \, dx[/tex]
This gives:
[tex]W =\int\limits^{60}_{30} {15x} \, dx[/tex]
Rewrite as:
[tex]W =15\int\limits^{60}_{30} {x} \, dx[/tex]
Integrate
[tex]W =15 \frac{x^2}{2}|\limits^{60}_{30}[/tex]
This gives:
[tex]W =15 *\frac{60^2 - 30^2}{2}[/tex]
[tex]W =15 *\frac{2700}{2}[/tex]
[tex]W =15 *1350[/tex]
[tex]W =20250N-cm[/tex]
Convert to Nm
[tex]W =\frac{20250Nm}{100}[/tex]
[tex]W =202.50Nm[/tex]
A rectangular prism has a base area of 2 square feet and a height of 5 feet. What
is the volume of the prism in cubic feet?
10
15
12
11
Submit
there are 750 spectator in the stadium of which 420 are women and the rest are men
Complete Question:
There are 750 spectator in the stadium of which 420 are women and the rest are men. What percent of the spectators are women?
Answer:
Percentage = 56%
Step-by-step explanation:
Given the following data;
Total number of people = 750
Number of women = 420
To find the percentage of women;
First of all, we would determine the number of male spectators (men);
Number of men = Total number of people - Number of women
Number of men = 750 - 420
Number of men = 330
Next, we find the percentage of women;
[tex] Percentage = \frac {420}{750} * 100 [/tex]
[tex] Percentage = \frac {42}{75} * 100 [/tex]
[tex] Percentage = 0.56 * 100 [/tex]
Percentage = 56%
Therefore, the percentage of the spectators that are women is 56%.
PLEASE HELP WILL MARK BRAINLIEST.Write the log equation as an exponential equation. You do not need to solve for x.
In (5) = 2x
Answer:
10x ÷ 5x=2x
10x ÷ 5x = 2x
10x÷ 5x = 2x
Answer:
[tex]e^{2x}=5[/tex]
Step-by-step explanation:
Recall that [tex]\log_b a=c\implies b^c=a[/tex].
In this case, we need to find the base of the logarithm. The logarithm [tex]\ln[/tex] denotes natural [tex]\log[/tex] with a base of [tex]e[/tex], a mathematical constant.
Therefore, we can re-write the equation as:
[tex]\log_e5=2x[/tex]
To write the equation as an exponential equation, recall the definition of log (first sentence of explanation):
[tex]\boxed{e^{2x}=5}[/tex]
what is the mean mark of 847 ÷ 30?
Answer:
Step-by-step explanation:
3p(2p - 9) - 2p(-9 + p)
Answer:
4p² - 9p
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3p(2p - 9) - 2p(-9 + p)
Step 2: Simplify
[Distributive Property] Distribute 3p: 6p² - 27p - 2p(-9 + p)[Distributive Property] Distribute -2p: 6p² - 27p + 18p - 2p²[Subtraction] Combine like terms (p²): 4p² - 27p + 18p[Addition] Combine like terms (p): 4p² - 9pSuppose a quadratic equation is given as follows:
(k – 1)x² + x + 1 = 0
Select all values of k for which the above equation has two real and unequal roots
0
.25
0.5
0.75
1
1.25
1.5
1.75
Answer:
k>1.25
Step-by-step explanation:
The given quadratic equation is :
(k – 1)x² + x + 1 = 0
We need to find all values of k for which the above equation has two real and unequal roots.
For a quadratic equation ax²+bx+c=0, for real and unequal roots,
b²-4ac>0
Here, a = (k-1), b = 1 and c = 1
Put all the values,
1²-4×(k-1)1>0
1-4k+4>0
5-4k>0
k>1.25
S, k can take values more than 1.25. Hence, it can take values 1.5, 1.75.
need an answer show work please thank you
Answer:
[tex]\text{C. }1[/tex]
Step-by-step explanation:
In the question, we're given that the notation [tex]\#\#(a,b,c)[/tex] produces a number [tex]a[/tex] less than the product of [tex]b[/tex] and [tex]c[/tex] raised to the [tex]a[/tex] power. Let the number produced be [tex]n[/tex]. As a mathematical equation, we can write this production as [tex]n=(bc)^a-a[/tex]
For [tex]\#\#(2, 5, x)[/tex], we can assign:
[tex]a\implies 2[/tex] [tex]b\implies 5[/tex] [tex]c\implies x[/tex]Substituting these values into [tex]n=(bc)^a-a[/tex], we get:
[tex]23=(5x)^2-2[/tex]
Add 2 to both sides:
[tex]25=(5x)^2[/tex]
Take the square root of both sides:
[tex]5=|5x|[/tex]
For [tex]y=|z|[/tex], there are two cases:
[tex]\begin{cases}y=z,\\y=-z\end{cases}[/tex]
Therefore, we have:
[tex]\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}[/tex]
The only answer choice applicable is [tex]\boxed{\text{C. }1}[/tex].
Consider the expression below. Assume the variable m represents an integer. 6m(3m + 21) Enter an expression in the box that uses the variable m and makes the equation true. (Simplify your answer completely. If no expression exists, enter DNE.) 6m(3m + 21) = 9 Given that m represents an integer, is 6m(3m + 21) divisible by 9?
Answer:
[tex](a)\ 6m(3m + 21) = 9(2m^2 + 14m)[/tex]
(b) Yes, it is divisible by 9
Step-by-step explanation:
Given
[tex]6m(3m + 21)[/tex]
Solving (a): Complete the blanks
[tex]6m(3m + 21) = 9 [\ ][/tex]
Expand the bracket
[tex]6m(3[m + 7]) = 9 [\ ][/tex]
[tex]6m*3(m + 7) = 9 [\ ][/tex]
Express 6m as 2m * 3
[tex]2m*3*3(m + 7) = 9 [\ ][/tex]
[tex]2m*9(m + 7) = 9 [\ ][/tex]
Rewrite as:
[tex]9 * 2m(m + 7) = 9 [\ ][/tex]
Multiply the bracket by 2m
[tex]9 * (2m^2 + 14m) = 9 [\ ][/tex]
Divide both sides by 9
[tex]2m^2 + 14m = [\ ][/tex]
Hence, the bracket will be filled with: [tex]2m^2 + 14m[/tex]
So:
[tex]6m(3m + 21) = 9(2m^2 + 14m)[/tex]
Solving (b): Is [tex]6m(3m + 21)[/tex] divisible by 9?
In (a), we have:
[tex]6m(3m + 21) = 9(2m^2 + 14m)[/tex]
The leading factor "9" implies that the expression is divisible by 9
Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
Let n represent the interger l, the three consective intergers are represented by
[tex]n[/tex]
[tex]n + 2[/tex]
[tex]n + 4[/tex]
The second one represent
[tex](n + 2) {}^{2} + 76 =( n + 4) {}^{2} [/tex]
Simplify both sides
[tex]n {}^{2} + 4n + 4 + 76 = {n}^{2} + 8n + 16[/tex]
[tex] {n}^{2} + 4n + 4 = {n}^{2} + 8n - 60[/tex]
[tex]4n + 4 = 8n - 60[/tex]
[tex]4n + 64= 8n[/tex]
[tex]64= 4n[/tex]
[tex]n = 16[/tex]
The intergers are 16,18,20
HELP ME ON THIS I HAVE MORE.
Answer:
The answer is 5 units.
Step-by-step explanation:
I just counted the squares
A stamp gets more expensive each year. It increases in value by 60 % each year. Wha
is the growth FACTOR?
9514 1404 393
Answer:
1.60
Step-by-step explanation:
The growth factor is 1 more than the growth rate:
1 + 60% = 1 + 0.60 = 1.60 = growth factor
PLEASE HELPPP !!!!! WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
128° because it is corresponding with <4
[tex] < 5 = \: < 3 \\ = \: < 4 \\ < 5 = 128 \degree[/tex]
A company that manufactures vehicle trailers estimates that the monthly profit for selling its midsize trailer is represented by function p, where t is the number of trailers sold. p(t)= -25t^3+625t^2-2500t Use the key features of function p to complete these statements. The company makes a profit when it sells _____trailers. The maximum profit of approximately $____ occurs when it sells approximately____ trailers.
Answer:
The answer is below
Step-by-step explanation:
The profit equation is given by:
p(t)= -25t³+625t²-2500t
The maximum profit is the maximum profit that can be gotten from selling t trailers. The maximum profit is at point p'(t) = 0. Hence:
p'(t) = -75t² + 1250t - 2500
-75t² + 1250t - 2500 = 0
t = 2.3 and t = 14.3
Therefore t = 3 trailers and t = 15 trailers
p(15) = -25(15³) + 625(15²) - 2500(15) = 18750
Therefore the company makes a maximum profit of approximately $18750 when it sells approximately 15 trailers.
Answer:
See below
Step-by-step explanation:
Since t is number of trailers, the domain includes only those values greater than 0.
On the relevant domain, the graph crosses the x-axis at the points (5,0) and (20,0). Between these points, the value of p(t) is positive. So the company makes a profit when it sells between 5 and 20 trailers.
On the positive interval between these points, the graph reaches a relative maximum when t roughly equals 14 and p(t) roughly equals $19,000.
So the maximum profit of approximately $19,000 occurs when it sells approximately 14 trailers.
A circular sinkhole has a radius of 12 meters. A week later, it has a diameter of 48 meters. How much greater is the circumference of the sinkhole compared to the previous week?
Answer:
B
Step-by-step explanation:
1) initial circumference
radius * 2 * pi = 24 * pi = 75,398224
2) final circumference
diameter * pi = 48 * pi = 150,796447
150,796447 - 75,398224 = 75.36 m
