Answers
Answer:
h = 2.12 , c = 6.93
Step-by-step explanation:
To calculate h:
Apply the cosine identity
[tex]cos\ x =\frac{base}{hypotenuse}\\\\cos\ 45=\frac{h}{3}\\\\0.707=\frac{h}{3}\\\\h=3(0.707)\\h=2.12\\[/tex]
To calculate c:
Apply the tangent identity
[tex]tan\ x=\frac{perpendicular}{base}\\\\tan\ 60=\frac{c}{4}\\\\1.732=\frac{c}{4}\\\\c=1.732(4)\\c=6.93\\[/tex]
C=6.9
Double check my answers using the picture below or by the long way (Pythagorean’s)
I suggest you memorize the drawings by heart because the 30-60-90 and the 45-45-90 right triangles are considered special in geometry and they will keep testing you on them until you graduate from university !
Hope it helps.
Related Questions
Evaluate 24 = (8-2).
Answers
Answer:
24 ÷ ( 8 - 2 )
= 24 ÷ 6
= 4
so, 4 is the answer
Answer:
on your question it says “=“ but on the picture it says “÷”
so for 24=(8-12) it would be 30
and for 24÷ (8-12) it would be -6
Step-by-step explanation:
Hope this helps, have a good day
pls help me. I have to state whether each graph is a function?.
Answers
Answer:
Step-by-step explanation:
1 no.. not continuous
2no.. not continuous
3 yes , over a certain range it is
4no b/c it fails the vertical line test.. there is more than one point on the x axis
5no multiple point on the x axis and not continuous
6 yes, over a certain range
Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3 and the volume is increasing at a rate of 5 cm^3/s. Find the rate of change of height at h = 15cm.
Answers
Answer:
[tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesGeometry
Volume of a Cone: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]Calculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{r}{h} = \frac{2}{3} \\\frac{dV}{dt} = 5 \ cm^3/s\\h = 15 \ cm[/tex]
Step 2: Rewrite Cone Volume Formula
Find the volume of the cone with respect to height.
Define ratio: [tex]\displaystyle \frac{r}{h} = \frac{2}{3}[/tex]Isolate r: [tex]\displaystyle r = \frac{2}{3} h[/tex]Substitute in r [VC]: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{2}{3}h)^2h[/tex]Exponents: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{4}{9}h^2)h[/tex]Multiply: [tex]\displaystyle V = \frac{4}{27} \pi h^3[/tex]Step 3: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{27} \pi \cdot 3 \cdot h^{3-1} \cdot \frac{dh}{dt}[/tex]Simplify: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{9} \pi h^{2} \frac{dh}{dt}[/tex]Step 4: Find Height Rate
Find dh/dt.
Substitute in known variables: [tex]\displaystyle 5 \ cm^3/s = \frac{4}{9} \pi (15 \ cm)^{2} \frac{dh}{dt}[/tex]Isolate dh/dt: [tex]\displaystyle \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} } = \frac{dh}{dt}[/tex]Rewrite: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} }[/tex]Evaluate Exponents: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (225 \ cm^2) }[/tex]Evaluate Multiplication: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{100 \pi cm^2 }[/tex]Simplify: [tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]draw a number line to divide 70 ÷5 =
Answers
Answer:
14
Step-by-step explanation:
In 70/5 the dividend is 70 and the divisor is 5 .
First draw a number line from zero to the dividend.
Next, starting from 70 skip count by the divisor backwards till you reach 0.
The numbers of skips taken to reach zero is the result, also called, the quotient. In this case there are 14 skips .
12 years ago, Catherine deposited $200 in a savings account that pays 7.25% simple
interest What is the balance in Catherinesco
Answers
Answer:
$374
Step-by-step explanation:
First you need to find how much money does the back pay per year
$200*7.25
=1450
1450/100
=14.5
Secondly you need to find how much does Catherine have in 12 years
14.5*12 years
=$174
Lastly add the money she already had 12 years ago to how much the bank payed in that 12 years
$200+$174
=$374
At the Italian deli, the sandwich maker cut 4 2/3 lb of turkey and 9 3/5 of roast beef. How many more pounds of roast beef were cut?
Answers
Answer:
4 14/15 more pounds of roast beef
Step-by-step explanation:
subtract 4 2/3 from 9 3/5
9 3/5 - 4 2/3= 4 14/15
So your answer is 4 14/15
You advance 3 levels in 15 minutes. Your friend advances 5 levels in 20 minutes. Are these rates proportional? Explain.
Answers
Answer:
no
Step-by-step explanation: the unit rate for 3 in 15 mins is 1 every 5 minutes.
the unit rate for the second one would be 1 for every 4 however
Answer:
No those rates are not proportionate
Step-by-step explanation:
15 divided by 3 = 5
20 divided by 5 = 4
Therefor proving that it took the person who did 5 levels took less time per level than the person who did 3.
You rent an apartment that costs $1800 per month during the first year, but the rent is set to go up $160 per year. What would be the monthly rent during the 9th year living in the apartment?
Answers
Answer:
$3240 I believe
Step-by-step explanation:
160 x 9 = 1,440
1,800 + 1,440 = 3,240
For each ångle pair, tell whether they are congruent or supplementary
Answers
Answer:
1&3 are supplementary
3&6 are congruent
4&5 are supplementary
2&3 are congruent
1&6 are supplementary (not sure about this one)
Step-by-step explanation:
What number is missing if this expression is equal to 12: (8 + ?) / (3/4
Answers
Answer:
The missing value is 1
Step-by-step explanation:
We need to find the missing value, if the expression is equal to 12.
The given expression is: [tex]\frac{(8+?)}{\frac{3}{4} }[/tex]
and the expression is equal to 12, so we can write: [tex]\frac{(8+?)}{\frac{3}{4} } = 12[/tex]
Solving to find the missing term
[tex]\frac{(8+?)}{\frac{3}{4} } = 12\\(8+?) \div (\frac{3}{4})=12\\Converting\:division\:sign\:to\:multiplication\:and\:reciprocating\:the\:term\\ (8+?) \times (\frac{4}{3})=12\\8+?=12 \times \frac{3}{4}\\8+?=3 \times 3\\8+? = 9\\? = 9-8\\?=1[/tex]
So, the missing value is 1
Which list shows the numbers in order from least to greatest?
479, 4.79, 4.709
479, 4.709, 4,79
4.709, 479, 4.79
4.79, 479, 4.709
4.79, 4.709, 479
Answers
y-x^2=5 written in function notation
Answers
Answer:
f(x) = x² + 5
General Formulas and Concepts:
Algebra I
Equality PropertiesFunction NotationStep-by-step explanation:
Step 1: Define
y - x² = 5
Step 2: Rewrite
Add x² to both sides: y = x² + 5Rewrite y: f(x) = x² + 5can you factorise 3x²+5x+2
Answers
Answer:
Yes, (3x + 2)(x + 1).
Step-by-step explanation:
1. You're going to need to find two numbers that add to equal 5. The best option here is 2 and 3.
2. Separate the equation into groups. Right now, you have [tex]3x^2 + 5x + 2[/tex]. To separate into groups, you write [tex](3x^2 + 3x) + (2x + 2)[/tex].
3. Now, from the first set of parenthesis, you can factor out 3x. This gets you [tex]3x(x + 1)[/tex]. The second set of parenthesis you can factor out the 2. This gets you [tex]2(x+1).[/tex]
4. Now, you see that you have (3x + 2)(x + 1).
Hope this helps! Let me know if you have any questions.
If Z is a standard normal variable find the probability. The probability that Z lies between -0.558 and 0.558
Answers
Answer:
0.4245
Step-by-step explanation:
The probability that Z lies between -0.558 and 0.558 can be written as;
P(-0.558 < z < 0.558) = P(z < 0.558) - P(z < -0.558)
Using z - distribution table, we have;
P(z < 0.558) = 0.7122
P(z < -0.558) = 0.2877
Thus;
P(z < 0.558) - P(z < -0.558) = 0.7122 - 0.2877 = 0.4245
At 1:00 P.M., oil begins leaking from a tank at a rate of (6 0.77t) gallons per hour. (Round your answers to three decimal places.) (a) How much oil is lost from 1:00 P.M. to 4:00 P.M.
Answers
Answer:
[tex]Amount = 8.31[/tex]
Step-by-step explanation:
Given
[tex]Rate = 6 + 0.77t[/tex]
Required
Determine the gallons of oil lost between 1pm to 4pm
[tex]Rate = 6 + 0.77t[/tex]
Where t represents number of hours
First, we need to calculate the duration between 1pm and 4m.
[tex]t = 4pm - 1pm[/tex]
[tex]t = 3\ hours[/tex]
Substitute 3 for t in [tex]Rate = 6 + 0.77t[/tex]
[tex]Amount = 6 + 0.77 * 3[/tex]
[tex]Amount = 6 + 2.31[/tex]
[tex]Amount = 8.31[/tex]
Hence, 8.31 gallons of oil has been lost
convert 240 yards per hour (yd/h) to yards per minute (yd/min).
Answers
9514 1404 393
Answer:
4 yd/min
Step-by-step explanation:
Change 1 hour to 60 minutes.
(240 yd)/(1 h) = (240 yd)/(60 min) = 4 yd/min
A screening examination was performed on 250 persons for Factor X, which is found in disease Y. A definitive diagnosis for disease Y among the 250 persons had been obtained previously. The results are charted below:
TEST RESULTS Disease Present Disease Absent
Positive for Factor X 40 60
Negative for Factor X 10 140
The specificity of this test is expressed as:________
Answers
Answer:
The specificity of this test is expressed as:________
70%.
Step-by-step explanation:
a) Data and Calculations:
TEST RESULTS Disease Present Disease Absent Total
Positive for Factor X 40 60 100
Negative for Factor X 10 140 150
Total 50 200 250
Negative for X and Disease Absent = 140/200 * 100
= 0.7 * 100
= 70%
b) The specificity refers to the percentage of people who test negative for a specific disease among a group of people who do not have the disease. No test is 100% specific because some people who do not have the disease X will test positive for it (false positive). Therefore, we are testing for the true negative, that the 140 people who tested out of the 200 people who do not have the disease.
write Thirty-four thousand.six hundred fifty-two as a base ten number
Answers
Answer:
34 652 is the number.Know find the ten place which is the (5).
PLZ HELP!!!!
Which group of numbers is in order from smallest to largest?
• 0.34, 45%, 13/25
• 27%, 3/4, 0.09
• 9/10, 0.8, 75%
• 0.24, 37%, 3/10
I will give you brainliest for correct answer... no scams though ! PLZ :(
Answers
Answer:
1)
Step-by-step explanation:
1 is the answer
I believe
Answer:
.34, 45, 13/25 im pretty sure
Step-by-step explanation:
Mary Anne's parakeet weighs 240g. Her cat weighs 3.1kg. What is the difference, in grams, of the weights of her pets?
Answers
Answer:
The cat weighs 2860 g more
Step-by-step explanation:
Convert the cats weight (3.1 kg) to grams.
Subtract the cats weight and the parakeets weight to find total.
In this case 3100 g (cats weight) - 240 g (parakeets weight) = 2860 g
A three digit number is selected at random from the set of all three digit numbers. The probability that the selected number has all the three digits the same is:__________.A.1/9B. 1/10C. 1/50D. 1/100
Answers
Answer:
1 /100
Step-by-step explanation:
Probability = (number of required outcomes / number of total possible outcomes)
Total possible outcomes = count of all 3 digit numbers ={100, 101,... 999} = 900
Required outcome = count of Three digit numbers with all 3 digits being the same = {111,222,333,444,555,666,777,888,999} = 9
Hence, probability that selected number has all 3 digits being the same :
9 / 900 = 1 /100
When packing a sultcase for a trip, the optimal welght of the suttcase Is 40 pounds. You aim for this weight with every trip you take. But your
sultcase's actual welght tends to vary by at most a certain number of pounds.
Part A. Write an absolute value inequality that models this relationship.
Part B. If the suitcase weight can vary by at most 7.5 pounds,what inequality can be used to find the range of acceptable weights for your suitcase?
Part C. Use the inequality from part B to determine the range of acceptable weights for the suitcase.
Part E. How would the inequality in part B change if you wanted to know the rate of weights that are unacceptable for your suitcase? Explain.
Part F. What is the solution for the inequality you created in part E?
Part H. What comparisons can you make between the two inequalities?
Part I. Will there ever be an instance where there is no solution to an absolute inequality? If yes,then what would the inequality look like?
Answers
Answer:
|x − 40| ≤ 7.5.
Step-by-step explanation:
The absolute value inequality |x − 40| ≤ y models the relationship between the acceptable weights of the suitcase and the amount it can vary.
If the suitcase weight can vary up to 7.5 pounds, then 7.5 can be substituted for y in the inequality:
|x − 40| ≤ 7.5.
This inequality can be used to find the range of acceptable weights of the suitcase.
Evaluate the expressions
4x+(-2), when x=3
Show your work here
Answers
Answer:
10
Step-by-step explanation:
PEMDAS MATH
no trolls pls help asap!!
Answers
if -1 < x < 0 which of the following has the smallest value?
(A) x^2
(B) x^3
(C) x^4
Answers
Answer: (B) x^3
Explanation:
If you compare the graphs of
y = x^2y = x^3y = x^4all on the interval -1 < x < 0, you'll find that y = x^3 is the smallest when x = -1
Squaring a negative number leads to a positive result, and similarly that happens with x^4 as well. This is because x^4 = (x^2)^2.
Plugging x = -1 into x^3 leads to y = -1 as a result.
Someone please tell me the answer
Answers
Answer:
30 times three
Step-by-step explanation:
because all the bottom number are multiplying buy three.
Maximus is playing a game. When he rolls the dice he wins if he gets an even number and loses if he gets an odd number. Which of the following statements is FALSE?
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution
b. Rolling an even number is considered a success
c. The count of rolling an even number can be approximated with a normal distribution
d. The count of rolling an odd number can be approximated with a normal distribution
Answers
Answer:
a. The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
Whenever we roll a fair dice, the possible outcomes are { 1, 2, 3, 4, 5, 6}. In this three numbers are even numbers, i.e. {2, 4, 6}.
The probability of getting an even number is [tex]$p (\text{even}) =\frac{3}{6} = \frac{1}{2}$[/tex]
Since each of the rolls is independent and each probability of getting even remains the same.
Using the central limit theorem, the sampling distribution of a large sample, usually more than 30 can be approximated by the normal distribution. A single roll of an even or odd number cannot be approximated by a normal distribution, it follows the Binomial distribution.
If number of rolls are large, then a normal approximation can be used.
Answer:
The count of rolling an odd number from a sample proportion size of 100 can be approximated with a normal distribution.
Step-by-step explanation:
Wendy drew a square. She then erased it and drew a second square whose sides were 3 times the sides of the first square. The area of the second square is k% greater than the area of the first square. What is k?
Answers
Answer:
x times x is x^2 for first area. second area is 3 times that so 3x times 3x you get 9x^2 for the second area. 9 - 1 times 100% would then be 800% larger.
The function F(x) varies inversely with x and f(x) = 25 when x = 6 what is f(x) when x= 18
Answers
Answer:
8.333
Step-by-step explanation:
F(x) α 1/ x
F(x) = k/x
F(x) = 25 ; x = 6
Lets use the information above to obtain the value of k
25 = k/6
k = 25 * 6 = 150
k = 150
Therefore, the value of f(x) when x = 18 will be :
Using the relation :
F(x) = k/x
k = 150, x = 18
F(x) = 150 / 18
F(x) = 8.333
Write an algebraic expression for the product of 2 and t.