Answers
Related Questions
State if the three numbers can be the measures of the sides of a triangle
5, 12, 10
Yes
No
Answers
Absolute value of -23/7
Answers
Two cylinders have the same volume. The first has a radius of 5cm and a height of 10 cm. The second has a radius of 10cm. The surface area of the first cylinder is and the surface area of the second i s
Answers
ANSWER
\(\begin{gathered} 1)150\pi \\ 2)250\pi \end{gathered}\)EXPLANATION
For the first cylinder;
\(\begin{gathered} r=5 \\ h=10 \end{gathered}\)Recall, the formula for calculating the surface area of a cylinder is;
\(A=2\pi rh+2\pi r^2\)Now, substitute the values for the first cylinder;
\(\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times5\times10+2\times\pi\times5^2 \\ =100\pi+50\pi \\ =150\pi \end{gathered}\)The volume of the first cylinder is calculated using the formula;
\(\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ \end{gathered}\)Substitute the values of r and h for the first cylinder;
\(\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ =\pi\times5^2\times10 \\ =\pi\times25\times10 \\ =250\pi \end{gathered}\)To get the surface area of the second cylinder, we need to calculate the height (h).
To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).
Hence;
\(\begin{gathered} V=250\pi \\ r=10 \\ V=\pi r^{2}h \\ 250\pi=\pi\times10^2\times h \\ h=\frac{V}{\pi \cdot \:r^2} \\ h=\frac{250\pi }{\pi 10^2} \\ =2.5 \end{gathered}\)Substitute the height to calculate the surface area is calculated thus;
\(\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times10\times2.5+2\times\pi\times10^2 \\ =50\pi+200\pi \\ =250\pi \end{gathered}\)A rectangular parking lot has an area of 1,650 square yards. The length of the parking lot is 55 yards. What is the width of the parking lot, in yards?
Answers
Answer:
w = 30 yd
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 EqualityGeometry
Area of a Rectangle: A = lw
l is lengthw is widthStep-by-step explanation:
Step 1: Define
A = 1650 yd²
l = 55 yd
w = unknown
Step 2: Solve for w
Substitute in variables [Area of a Rectangle]: 1650 yd² = (55 yd)(w yd)[Division Property of Equality] Divide 55 yd on both sides: 30 yd = wRewrite: w = 30 ydSimplify i^41 (please help me)
Answers
Answer:
i
Step-by-step explanation:
Answer: Choice A) i
====================================================
Explanation:
Let's look at the pattern of powers of i
i^0 = 1i^1 = ii^2 = (sqrt(-1))^2 -1i^3 = i*i^2 = i*(-1) = -ii^4 = (i^2)^2 = (-1)^2 = 1We loop back to 1, and the process starts all over again. The cycle is 4 units long. Ie, the pattern repeats every 4 terms.
What this means is that we can use remainders to quickly figure out something like i^41 without having to use a calculator or tons of paper.
Dividing 41/4 leads to a quotient of 10 and a remainder of 1. We only care about the remainder. The remainder 1 means i^41 = i^1 = i
Note how 41 and 1 lead to the same remainder when we divide by 4.
PLEASE HELP AND EXPLAIN HOW TO DO THIS
Find Sn for the given geometric series.
1=0.11, 5=895.956875, =9.5
Answers
Answer:
1001.35
Step-by-step explanation:
Assuming
n
=
5
for which sum to be found.
We know sum of geometric series up to
n
th term is
S
n
=
a
1
⋅
r
n
−
1
r
−
1
Here
a
1
=
0.11
,
r
=
9.5
,
n
=
5
∴
S
5
=
a
1
⋅
r
5
−
1
r
−
1
=
0.11
⋅
9.5
5
−
1
9.5
−
1
≈
1001.35
[Ans]
suppose a research report states that the result of a between subjects one-way anova is f (3, 32) = 3.47 should the researcher reject the null hypothesis if using alpha = .05
Answers
Based on the given information, the researcher should not reject the null hypothesis if using an alpha level of 0.05.
In hypothesis testing, the null hypothesis is typically assumed to be true until there is sufficient evidence to reject it. To determine whether to reject the null hypothesis, researchers often compare the calculated F-value from an ANOVA test with the critical F-value. The critical F-value is based on the significance level (alpha) chosen for the test. In this case, the given F-value is 3.47 with degrees of freedom (3, 32), indicating that there are three groups and a total of 32 observations. To make a decision, the researcher needs to compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, the null hypothesis is rejected. However, if the calculated F-value is less than or equal to the critical F-value, the null hypothesis is not rejected. Since the critical F-value corresponding to alpha = 0.05 is not provided in the question, we cannot determine whether the null hypothesis should be rejected.
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A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.
Answers
The dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
Let's start by finding the formula for the cost of the container in terms of its dimensions.
The volume of the cylinder is given as 600 cubic centimeters, so we have:
πr^2h = 600
where r is the radius of the cylinder and h is its height. Solving for h, we get:
h = 600 / (πr^2)
The surface area of the cylinder is given by:
A = 2πrh + 2πr^2
Substituting h in terms of r, we get:
A = 2πr(600/(πr^2)) + 2πr^2
= 1200/r + 2πr^2
The cost of the container is the sum of the cost of the styrofoam sides and bottom and the cost of the paper top. Let's call the radius of the paper top R, and assume that the height of the cylinder is greater than or equal to the radius of the paper top, so that the top can be completely covered with paper. Then the cost of the container is:
C = 0.04(2πrh + πr^2) + 0.05(πR^2)
Substituting h in terms of r, we get:
C = 0.08πr(600/(πr^2)) + 0.04πr^2 + 0.05πR^2
= 4.8/r + 0.04πr^2 + 0.05πR^2
To minimize the cost, we need to find the values of r and R that minimize the cost function C. To do this, we take the partial derivatives of C with respect to r and R, and set them equal to zero:
dC/dr = -4.8/r^2 + 0.08πr = 0
dC/dR = 0.1πR = 0
Solving for r and R, we get:
r = ∛(60/π) ≈ 2.78 cm
R = 2.5 cm
We can check that these values give us a minimum by checking the second derivatives:
d^2C/dr^2 = 9.6/r^3 + 0.08π > 0 (minimum)
d^2C/dR^2 = 0.1π > 0 (minimum)
Therefore, the dimensions of the cylinder that minimize the production cost are:
radius = approximately 2.78 cm
height = 600 / (πr^2) ≈ 7.14 cm
paper top radius = 2.5 cm
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On Saturday, some adults and some children were in a theatre.
The ratio of the number of adults to the number of children was 7:2
Each person had a seat in the Circle or had a seat in the Stalls.
of the children had seats in the Stalls.
124 children had seats in the Circle.
There are exactly 3875 seats in the theatre.
On this Saturday, what percentage of the seats had people sitting on them?
+
Total marks: 5
Answers
The ratio of adults indicates that there are 7 adults foe every 2 children,
given the number of children, the number of people can be found.
The percentage of seats that had people sitting on them is 72%Reasons:
The given parameters are;
Ratio of adults to children = 7 : 2
The proportion of children that had sit in the stalls = 4/5
Number of children that had sit in the Circle = 124 children
Number of seats at the theater = 3,875
Required:
The percentage of the sits that had people sitting on them.
Solution:
Let x represent the number of children, we have;
Number of children in the stalls = \(\displaystyle \frac{4}{5} \cdot x\)
\(\displaystyle Number \ of \ children \ in \ the \ circle = \mathbf{x - \frac{4}{5} \cdot x} = 124\)
Therefore;
\(\displaystyle x=\frac{124}{1 - \frac{4}{5} \times 1} = \mathbf{620}\)
The number of children, x = 620 children
\(\displaystyle \mathbf{ \frac{Number \ of \ adult}{Number \ of \ children}} = \frac{7}{2}\)Therefore;
\(\displaystyle \frac{Number \ of \ adult}{620} = \frac{7}{2}\)
2 × Number of adults = 7 × 620
Number of adults = 7 × 620 ÷ 2 = 2,170
The total number of persons, n = Number of children + Number of adults
Therefore;
n = 2,170 + 620 = 2,790
\(\displaystyle Percentage \ of \ sits \ with \ people = \mathbf{ \frac{2,790}{3,875} \times 100} = \underline{72 \%}\)
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can you help me with this please
Answers
Answer:
part a is a and c
part b is sine
Step-by-step explanation:
I hope this helped :)
K = 3/5 is a solution to the inequality 15k + < 15
Answers
Since K = 3/5 satisfies this inequality, we can confirm that K = 3/5 is a solution to the inequality 15k + < 15.
To determine whether K = 3/5 is a solution to the inequality 15k + < 15, we can substitute K = 3/5 in the inequality and simplify as follows:15(3/5) + < 15
Multiply the coefficients15 * 3 = 455/5 + < 15
Simplify the fraction by multiplying the denominator by 3 to get a common denominator.15/1 is equivalent to 45/3. Thus, 45/3 + < 75/3
Simplify the left-hand side to get: 15 + < 75/3
Simplify 75/3 to get: 25Thus, 15 + < 25
We can verify that K = 3/5 is a solution to the inequality because 15(3/5) is less than 15. This implies that K = 3/5 satisfies the inequality.
Since the solution is 15(3/5) + < 15, which simplifies to 15 + < 25, and since K = 3/5 satisfies this inequality, we can confirm that K = 3/5 is a solution to the inequality 15k + < 15.
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payments of $1400 each year for 8 years at 6ompounded annually
Answers
If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.
To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.
To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).
Plugging in the values, we have:
FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06
≈ $12,350
Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.
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Write an equation with the following: m=1/2 b=-9
Answers
Answer: y = 1/2x - 9
Step-by-step explanation:
Slope formula is y = mx + b
Substitute
y = 1/2x - 9
Answer:
y = 1/2x - 9
Step-by-step explanation:
Substitute for y=mx+b
What expression is equivalent to 24a+(-26b)-13a+12b?
Answers
The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
What is algebraic expression ?
An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.
Examples of algebraic expressions include "3x + 4y", "2a^2 - 5b", and "(x + 3)(x - 2)".
Given expression ,
24a+(-26b)-13a+12b
= 24a - 13a +12 b - 26b
= 11a - 14b
Therefore, The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
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A lecture hall has 50 seats.
43 seats are occupied and 7 seats are empty.
Use this information to answer the questions below.
Answers
Answer:14% of the seats are empty
Step-by-step explanation:
7/50 = ?/100
50×2=100
so 7×2=?
?=14
14/100=14%
Ariana is going to invest in an account paying an interest rate of 1.9% compounded monthly. How much would Ariana need to invest, to the nearest ten dollars, for the value of the account to reach $110,000 in 14 years?
Answers
Answer:
110000=p(1+0.019)^168
23.62p=110000
p=4660
credit: sqdancefan
Answer:
84330
Step-by-step explanation:
The compound interest formula gives the value of an investment.
A = P(1 +r/n)^(nt)
where principal P is invested at annual rate r compounded n times per year for t years. Using your given values, we can solve for P.
110,000 = P(1 +0.019/12)^(12·14)
P = 110,000/(1 +0.019/12)^(12·14) ≈ 110,000/1.00158333...^168
P ≈ 110,000/1.30446
P ≈ 84326.04 ≈ 84,330 . . . . dollars
One card is drawn from deck of 15 cards numbered through 15_ Find the following probabilities (Enter your probabilities as fractions.) (a) Find the probability that the card is even and divisible by 3. (b) Find the probability that the card even or divisible by 3
Answers
a) The probability of drawing a card that is even and divisible by 3 is 2/15.
b) The probability of drawing a card that is even or divisible by 3 is 11/15.
(a) To find the probability that the card is even and divisible by 3, we need to determine the number of cards that satisfy both conditions and divide it by the total number of cards.
The numbers that are even and divisible by 3 within the range of 1 to 15 are 6 and 12. Therefore, there are 2 cards that meet both conditions.
Since there are 15 cards in total, the probability of drawing a card that is even and divisible by 3 is 2/15.
(b) To find the probability that the card is even or divisible by 3, we need to determine the number of cards that satisfy either condition and divide it by the total number of cards.
The numbers that are even within the range of 1 to 15 are 2, 4, 6, 8, 10, 12, and 14, which are a total of 7 cards. The numbers divisible by 3 within the same range are 3, 6, 9, 12, and 15, which are a total of 5 cards. However, we should not count 6 twice since it satisfies both conditions.
Therefore, there are 7 + 5 - 1 = 11 cards that are either even or divisible by 3.
Since there are 15 cards in total, the probability of drawing a card that is even or divisible by 3 is 11/15.
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What outcome is likely to occur for a hypothesis test evaluating a treatment that has a very large and robust effect?
Answers
For the given statement, we have to correctly rejecting the null hypothesis.
According to the statement
we have to find the outcome when hypothesis test evaluating a treatment that has a very large and robust effect.
For this purpose, we know that the
A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
And according to the given statement it is clear that the by this we have to rejected this hypothesis.
because this treatment and the large effects are not possible for the independent values of the hypothesis.
In other words, we can say that the we have to correctly rejecting the null hypothesis.
So, For the given statement, we have to correctly rejecting the null hypothesis.
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Based on the information in the two-way table, what is the probability that a person
selected at random both bikes and runs?
Round your answer to the nearest tenth of a percent.
Do not bike
Run
Do not run
Bike
42
6
7
4
Answers
The probability that a person selected at random both bikes and runs is 6.8%.
To find the probability that a person selected at random both bikes and runs, we need to determine the number of individuals who both bike and run and divide it by the total number of individuals in the sample.
Looking at the two-way table, the number in the "Bike" and "Run" category is 4. This represents the number of individuals who both bike and run.
The total number of individuals in the sample can be found by summing up the values in all four cells of the table:
42 + 6 + 7 + 4 = 59
Therefore, the probability that a person selected at random both bikes and runs is:
Probability = (Number of individuals who both bike and run) / (Total number of individuals)
Probability = 4 / 59
Using a calculator, the value of this probability is approximately 0.0678.
Rounding to the nearest tenth of a percent, the probability is approximately 6.8%.
Therefore, the probability that a person selected at random both bikes and runs is 6.8%.
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what is the slope of the line containing the point( -9,2) and (3,14)
Answers
Answer:
the slop is 1
Step-by-step explanation:
hop that help
The table shows the results of an experiment in which three coins were tossed.
What is the experimental probability that at least two of the coins will be heads? The theoretical probability?
Answers
The experimental probability that at least two heads would be gotten is 11 / 25.
The theoretical probability that at least two heads would be gotten is 1/2.
What are the probabilities?Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Experimental probability = number of times at least two heads would be gotten / total number of tosses
( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25
Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes
4 / 8 = 1/2
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Find the value for m
-10 + 59 = 5m = 7 + 3m
Answers
-49= 5m=7+3m
5m=56+3m
2m=56
m=28
Does someone know the answers to question 12 and 13 ??? GIVING 30 POINTS
Answers
Answer:
Step-by-step explanation:
For 12 if its a parrell line then the slope of the two lines have to be the same. Since the slope is 3/5 then the answer is A because the slope in A is also 3/5
for 13 if its perpendicular, then the slope has to be the opposite sign and flipped. so for example if its a negative then the slope has to be a positive and if the slope is 1/2 you have to flip it which is 2/1 and 2/1 equals 2.
so in this one if the slope is 3/5 we have to flip it making it 5/3 and the opposite of a positive is a negative so it would be -5/3, so the answer is C.
Answer:
12. A
13. C
Step-by-step explanation:
12. to be parallel needs same slope
13. to be perpendicular flip slope and if positive change to negative
Hans can choose Plan A or Plan B for his long distance charges.
Answers
The plan that costs less if Hans makes 300 minutes of long distance calls is Plan A by $ 4.
The number of long distance minutes till the plans cost the same is 350 minutes.
If the time spent on long distance calls is more than this amount, the plan that costs less is Plan B.
How to find the plan cost ?The cost per plan can be seen on the graph. At 300 minutes of long distance calls, Plan A costs $ 24 and plan B costs $ 28 so the cheaper plan is Plan A by :
= 28 - 24
= $ 4
The number of minutes till they cost the same is 350 minutes which is where they intercept and after this, Plan B will cost less.
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3 pts
Question 1
You find a crystal in the shape of a prism. Find the volume of the crystal.
The point Bis directly underneath point E, and the following lengths are known:
• From A to B: 2 mm
• From B to C:3 mm
. From A to F: 6 mm
• From B to E: 10 mm
. From C to D: 7 mm
• From A to G: 4 mm
G
А
B
What is the area of the base? ( 1 point) Explain or show your reasoning. (2 points)
Answers
The Volume of crystals is 160 mm³ while the area of the base is 20 mm².
VolumeVolume is the amount of space occupied by a three dimensional shape or object.
Area of triangle = (1/2) * DF * height
Height = 10 - 6 = 4 mm, DF = AC = AB + BC = 2 + 3 = 5 mm
Area of triangle = (1/2) * 5 * 4 = 10 mm²
Volume of triangle prism = Area of triangle * AG = 10 * 4 = 40 mm³
Volume of rectangular prism = A to F * AC * AG = 6 * 5 * 4 = 120 mm³
Volume of crystals = 120 + 40 = 160 mm³
Area of base = AC * AG = 5 * 4 = 20 mm²
The Volume of crystals is 160 mm³ while the area of the base is 20 mm².
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Selecting a US State Choose one of the 50 states at random. a. What is the sample space? [Type your answer here] b. What is the probability that it begins with M? [Type your answer here] c. What is the probability that it doesn't begin with a vowel?
Answers
Sample space of randomly selecting a US state is 50, the probability that the US state begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.
a. What is the sample space?The sample space for randomly selecting one of the 50 US states is 50, i.e., the list of the 50 states.
b. What is the probability that it begins with M?The number of states that begin with M is 8. Therefore, the probability that the randomly selected US state begins with M is 8/50 or 4/25.
c. What is the probability that it doesn't begin with a vowel?There are 20 US states that don't begin with a vowel. Therefore, the probability that a randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.
Randomly selecting a US state requires knowing the sample space, which in this case is 50. A sample space represents all possible outcomes of a random experiment. Therefore, the sample space for this problem represents the list of all 50 US states that can be randomly selected. The probability that a randomly selected US state begins with M can be calculated by dividing the number of states that begin with M by the total number of states. There are 8 US states that begin with M, hence, the probability of selecting a state that begins with M is 8/50 or 4/25. Finally, the probability that the randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.
In conclusion, the sample space of selecting a US state randomly is 50, the probability that it begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.
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Does the triangle inequality theorem apply to all equilateral triangles?
Answers
Yes, triangle inequality theorem apply to all equilateral triangles.
Describe Triangle inequality theorem:The triangle inequality theorem explains the relation between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.
So Triangle inequality theorem is not only valid for all equilateral traingles but it is valid for all traingles.
A Triangle is only formed is if follows Triangle inequality theorem so every equilateral triangle needs to follow this theorem.
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find the common difference of the arithmetic sequence 15,22,29, …
Answers
Answer:
7
Step-by-step explanation:
You want the common difference of the arithmetic sequence that starts ...
15, 22, 29, ...
Difference
The common difference is the difference between a term and the one before. It is "common" because the difference is the same for all successive term pairs.
22 -15 = 7
29 -22 = 7
The common difference is 7.
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Simplify. (x3 + 2x − 3)(x4 − 3x2 + x)
(please provide a step-by-step explanation and answer. I don't just need the answer I need to understand how to do this)
x12 − 3x6 − x4 + x3 + 3x2 − x
x12 − 3x6 − x4 + x3 − 15x2 − x
x7 − x5 − 2x4 − 6x3 + 11x2 − 3x
x7 − 5x5 − 2x4 − 6x3 + 11x2 − 3x
Answers
Step-by-step explanation:
x¹²-3x6-x⁴+2x⁴-6x³+2x²-3x⁴+9x²-3x
x¹²-3x6-2x⁴-6x³+11x²-3x
solve for x round to the nearest tenth
