Answer:
37.68 in.^3
Step-by-step explanation:
diameter = 4 in.
radius = diameter/2 = 2 in.
height = 9 in.
[tex] V = \dfrac{1}{3}\pi r^2 h [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \blue{37.68~in.^3} [/tex]
The points P and Q have coordinates (-1, 6) and (9, 0) respectively.
The line l is perpendicular to PQ and passes through the mid-point of PQ.
Find an equation for l, giving your answer in the form ax + by + c =0, where a, b and c are integers.
Answer:
[tex]3y - 5x +11=0[/tex]
Step-by-step explanation:
Given
[tex]P(x_1,y_1) = (-1,6)[/tex]
[tex]Q(x_2,y_2) = (9,0)[/tex]
Required
The equation of l
First, calculate the slope (m) of PQ
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{0-6}{9--1}[/tex]
[tex]m = \frac{-6}{10}[/tex]
[tex]m = \frac{-3}{5}[/tex]
Since l is perpendicular to PQ, the slope of l is:
[tex]m_2 = -\frac{1}{m}[/tex]
[tex]m_2= -\frac{1}{-3/5}[/tex]
[tex]m_2 = \frac{5}{3}[/tex]
Next, calculate the midpoint of PQ
[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]
[tex]M = \frac{1}{2}(-1+9,6+0)[/tex]
[tex]M = \frac{1}{2}(8,6)[/tex]
[tex]M = (4,3)[/tex]
The equation of l is:
[tex]y = m(x -x_1) + y_1[/tex]
[tex]y = \frac{5}{3}(x -4) +3[/tex]
Multiply through by 3
[tex]3y = 5(x -4) +9[/tex]
Open bracket
[tex]3y = 5x -20 +9[/tex]
[tex]3y = 5x -11[/tex]
Rewrite as:
[tex]3y - 5x +11=0[/tex]
Suppose that each student at a university has one of 4 expected graduation years and one of 21 majors. How many students must be enrolled to guarantee 2 graduations in the same year and major?
Answer:
The correct answer is "168 students".
Step-by-step explanation:
According to the question,
Graduation probability,
[tex]P_g=\frac{1}{4}[/tex]
Major probability,
[tex]P_m=\frac{1}{21}[/tex]
Now,
The probability of having both graduation as well as major will be:
= [tex]\frac{1}{4}\times \frac{1}{21}[/tex]
= [tex]\frac{1}{84}[/tex]
hence,
The number of students having guarantee two graduations throughout the same year and major will be:
⇒ [tex]\frac{x}{84}=2[/tex]
By applying cross-multiplication, we get
⇒ [tex]x = 84\times 2[/tex]
⇒ [tex]=168[/tex]
for what value of x does 4x=(1/8)^x+6?
Answer please help
A. -15
B. -3
C. 3
D. 15
Im sorry but what I got was x=1.5 I don't know if this helps or not.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per
year, compounded monthly. Give your answer accurate to 2 decimal places.
Preview
years.
Answer:
The time required is of 17.53 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.
This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]
[tex](1.0033)^{12t} = 2[/tex]
[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]
[tex]12t\log{1.0033} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]
[tex]t = 17.53[/tex]
The time required is of 17.53 years.
50 + x + 10 + 8x + 2x =650
what is the value of x?
Answer:
x = 590/11
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
50 + x + 10 + 8x + 2x = 650
Step 2: Solve for x
[Addition] Combine like terms: 11x + 60 = 650[Subtraction Property of Equality] Subtract 60 on both sides: 11x = 590[Division Property of Equality] Divide both sides by 11: x = 590/11Answer:
x= 590/11
Step-by-step explanation:
Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
please help meeeee!!
Step-by-step explanation:
[tex]\begin{aligned} -5x+4y &= 3\\\\ x&=2y-15 \end{aligned}[/tex]
Solve the following system of equations and show all work. y = 2x2-3 y = 7x + 1 (10 points)
Answer:
x = -1/2 , y = -5/2
x = 4, y = 29
Step-by-step explanation:
y = 2x² - 3
y = 7x + 1
------------------
set equal
2x² - 3 = 7x + 1
Subtract 7x + 1 from both sides
2x² - 7x - 4 = 0
Factor
(2x + 1)(x - 4) = 0
x = {-1/2, 4}
For x = -1/2
y = 7(-1/2) + 1
y = -5/2
(-1/2 , -5/2)
For x = 4
y = 7(4) + 1
y = 29
(4, 29)
PLEASE HELP ASAP!!! What is the range of the function shown on the graph?
(The graph is below)
Answer:
-6 < y < ∞
Step-by-step explanation:
The range is the values that y can take
y goes from almost -6 to infinity ( there is an asymptote at -6)
-6 < y < ∞
if the volume of a Sphere is 36 pie cm³. then find its radius
I will give brainliest
Answer: r = 3
Step-by-step explanation:
V=(4/3)πr^3 (this is the formula to identify a volume of the sphere. Since we know that V = 36π, add it into the following formula like so:
36π = (4/3)πr^3; from here we can cancel out the π
36 = (4/3)r^3; multiply both sides by 3/4
27 = r^3;
the final answer is r = 3.
the temperature at 6 pm in frost frozen antarctica was -37 if the tem dropped 8 1 /2 c uring the next hour what was the the temp at 7 pm
Answer:
-45 1/2
Step-by-step explanation:
I need a math genius please
!!WILL MARK BRAINLIEST!! PLEASE SOMEONE HELP!! IM TRYING TO PREPARE FOR MATH CAMP AND THEY GAVE US THIS PROBLEM AND I CANT FIND ANYTHING LIKE IT!!
Answer:
How long is the [shirt] in the air? 3 seconds
How many seconds after launching is the t-shirt at 17 feet? 0.25 seconds
Step-by-step explanation:
Formula to represent the shirt's flight path (given): [tex]h=-16t^2+vt+c[/tex], where [tex]h[/tex] is the height of the shirt, [tex]v[/tex] is the initial velocity of the shirt, [tex]c[/tex] is the shirt's starting height, and [tex]t[/tex] is elapsed time since launch.
The function forms a parabola concave down. Since the shirt is caught at 17 feet, we want to second x-coordinate of a point with a y-coordinate of 17 that the function passes through. This is because the shirt was caught going down, not up.
Therefore, let [tex]h=17[/tex]:
[tex]17=-16t^2+52t+5,\\\\-16t^2+52t-12=0,\\\\ y= \frac{-52\pm\sqrt{52^2-4(-16)(-12)}}{2(-16)},\\\\y=\frac{1}{4},\boxed{y=3}[/tex].
The second x-coordinate is the larger of the two and therefore the shirt was in the air for 3 seconds.
However, the first time the shirt reaches a height of 17 feet is on its way up, which occurs at 1/4 or 0.25 seconds (the first x-coordinate). Therefore, the t-shirt reached a height of 17 feet 0.25 seconds after launching.
You put $600 in a savings account. The account earns 6% simple interest per year.
a. What is the interest earned after 10 years?
b. What is the balance after 10 years?
what is the area of a rectangular driveway measuring 20 feet long and 15 feet wide?
Answer:
300 square feet
Step-by-step explanation:
Area is found by multiplying the length and width of a surface
Alec bakes spherical rolls of bread. Each roll is about 8cm
wide. What is the approximate volume of each roll? Use
3.14 to approximate a.
Answer:
Step-by-step explanation:
2143.57
Two angles are complementary. One angle measures 60 degrees. What is the measure of the other angle?
I'm not sure if its A.
Answer:
30
Step-by-step explanation:
Complementary angles add to 90
x+60 = 90
x+60-60 = 90-60
x = 30
Answer: A
Step-by-step explanation:
Complementary angles sum up to 90 degrees. Thus, we can write that:
90=angle1+angle2
90-angle1=angle2
90-60=angle2
angle2=30
Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct
Answer:
Option C
Step-by-step explanation:
n = 81
s2 = 625
H0: σ2 = 500
Ha: σ2 ≠ 500
Test Statistics X^2 = (n-1)s^2/ σ2 = (81-1)*625/500
X^2 = 100
P value = 0.0646 for degree of freedom = 81-1 = 80
And X^2 = 100
At 95% confidence interval
Alpha = 0.05 , p value = 0.0646
p < alpha, we will reject the null hypothesis
At 95% confidence, the null hypothesis
Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.
Carpeted Un-Carpeted
15.9 8.1 15 7.2 10.4 6.1
11.2 16 11.2 6.8 11.3 6.8
8.6 10 12.1 6.3
Requried:
State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.
Answer:
The null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:
H[tex]_{0}[/tex]: μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].
H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
Step-by-step explanation:
In the question, the given assertion is that carpeted rooms have more bacteria than uncarpeted rooms, i.e. μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
The assertion made in the question can either be the null hypothesis (H[tex]_{0}[/tex]) or the alternate hypothesis (H[tex]_{1}[/tex]). An equality must be present in the null hypothesis. The alternative hypothesis expresses the exact opposite of the null hypothesis if the claim is the null hypothesis.
Therefore, the null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:
H[tex]_{0}[/tex]: μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].
H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
What is the domain of the square root function graphed below?
Answer:
Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.
Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.
Step 3: Write the answer using interval notation.
Which of the following best describes the equation below? y = x + 8 OA. function only B. both a relation and a function Oc. neither a relation nor a function OD. relation only?
9514 1404 393
Answer:
B. both a relation and a function
Step-by-step explanation:
Every linear equation with defined slope is both a relation and a function.
__
Only a vertical line of the form x=constant is linear equation that is a relation, but not a function.
Consider a fishery in which harvesting is taking placeat a constant rateh. The population at the fisherywill be modeled by
dP/dt = kP- h
Required:
Find the general solution to this DE.
Answer:
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
Step-by-step explanation:
We are given the following differential equation:
[tex]\frac{dP}{dt} = kP - h[/tex]
Solving by separation of variables:
[tex]\frac{dP}{kP-h} = dt[/tex]
Integrating both sides:
[tex]\int \frac{dP}{kP-h} = \int dt[/tex]
On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then
[tex]\frac{1}{k} \ln{kP-h} = t + K[/tex]
In which K is the constant of integration.
[tex]\ln{kP-h} = kt + K[/tex]
[tex]e^{\ln{kP-h}} = e^{kt + K}[/tex]
[tex]kP - h = Ke^{kt}[/tex]
[tex]kP = Ke^{kt} + h[/tex]
[tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
Q. A board that measures feet long is cut into 6 equal pieces. What is the length of each piece?
A. 1} inches
B. 3 inches
C. 3 inches
D. 9 inches
QUESTION :- . A board that measures feet long is cut into 6 equal pieces. What is the length of each piece?
A. 1 inches
B. 3 inches
C. 2 inches
D. 9 inches
ANSWER:- 1 FEET -->12 INCH
ATQ ->
1 FEET IS divided into 6 parts so
1 feet = 12 inches
[tex] \frac{1}{6} feet = \frac{12}{6} inches \\ \frac{1}{6} feet = 2 inches [/tex]
so each part will be equal to 2 inches
1 ft = 12 in
12 inch can be devided into 6 equal parts resulting in 2 inches each.
I guess you mistyped either B or C..
hope it helps
kind regards
Alex
A small town experienced explosive population increase. Originally the town had population 170. Within 3 years, the town's population increased by 400%. What's the town's current population
Answer:
850
Step-by-step explanation:
Given that :
Initial population = 170
Percentage rise in population within 3 years = 400%
Hence, the current population of the town will be ;
Current population = Initial population * (1 + rate)
Current population = 170(1 + 400%)
Current population = 170(1 + 4)
Current population = 170(5)
Current population = 850
HELP ASAP I WILL GIVE BRAINLIST
A = {1, 3, 4, 5, 7, 9}
B = {1, 2, 4, 6, 8, 10}
List the outcomes of A ∪ B? What does this represent?
List the outcomes of A ∪ B? What does this represent?
Answer:
A U B={1,2,3,4,5,6,7,8,9,10} represents A union B
(includes all the members of set Sand the members of set Bout together, do not repeat anyone that comes twice)
A n B={1,4} represents A interception B( this refers to the members that sets A and B have in common)
Answer:
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
Step-by-step explanation:
A = { 1 , 3 , 4 , 5 , 7 , 9 }
B = { 1 , 2 , 4 , 6 , 8 , 10 }
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
It represents the whole numbers between 0 and 11
[ A ∪ B is the elements of both A and B , without any repetition ]
A ∩ B = { 1 , 4 }
It represents the common numbers in both A and B
Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n cubed minus n Over n squared + 5 n EndFraction?
Answer:
The answer is " The sequence converges to infinity. "
Step-by-step explanation:
Given:
[tex]\to a_n=\frac{n^3-n}{n^2+5n}[/tex]
[tex]\lim_{n \to \infty} a_n= \lim_{n \to \infty} \frac{n^3-n}{n^2+5n}[/tex]
[tex]= \lim_{n \to \infty} \frac{n(n^2-1)}{n(n+5)}\\\\= \lim_{n \to \infty} \frac{(n^2-1)}{(n+5)}\\\\= \lim_{n \to \infty} \frac{n(n-\frac{1}{n})}{n(1+\frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n-\frac{1}{n})}{(1+\frac{5}{n})}\\\\[/tex]
Denominator[tex]= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1[/tex]
Numerator [tex]=\lim_{n\to \infty}n-\frac{1}{n}=\infty[/tex]
[tex]\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty[/tex]
what type of data states that every value in the set is a number
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Step-by-step explanation:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
As preparation for designing a new line of business wear, a clothing manufacturer asked a large sample of department store customers, "What is your favorite
color of dress shirt?" The ple chart below summarizes their responses.
(a) Which color was chosen by approximately one fourth of
the customers?
Answer:
white
Step-by-step explanation:
if you cut the shape in half both ways it makes white take up a fourth.
3.42x16.5 show your work plz
Answer:
= 56.43
Step-by-step explanation:
= 3.42 × 16.5
multiply the numbers= 56.43
which equation is correctly rewritten to solve for x?
What proportion of families own as opposed to rent their home? To find out, an urban planner selected a random
sample of 400 families in a large city to participate in a survey about homeownership. Of the 362 families that
responded to the survey, 42% reported that they own their home. Which of the following statements about the
survey results is true?
O A suitable estimate of all families who own their home is 42%.
The survey suffers from voluntary response bias and may not accurately represent the population.
O Only 362 responses cannot provide a suitable estimate of families who own their home.
O The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Mark this and return
Save and Exit
fyext
Submit
Answer:
A suitable estimate of all families who own their home is 42%.
Step-by-step explanation:
42% reported that they own their home.
This means that the sample proportion is of 42%. So that an estimate for the percentage of all families who own their home is of 42%., and that the first option is correct.
Answer:
The correct answer is: The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Step-by-step explanation:
I just took the review test. The person above me is wrong
If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x).
True or false?
Answer:
False
Step-by-step explanation:
Take the point (2, 3) = (x, y)
Rotated 90º clockwise (3, -2) = (y, -x)
Rotated 90º counter clockwise (-3, 2) = (-y, x)
Neither rotation becomes (-3, -2)