Answer:
A waterfall has a height of 1500 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet per second. The height, h, of the pebble after t seconds is given by the equation h =−16t^2+24t+1500. How long after the pebble is thrown will it hit the ground?
Pebble will hit the ground after 10.46 seconds.
Step-by-step explanation:
Given:
The height, "h" of the pebble after t seconds, "h" = −16t^2+24t+1500
We have to find the time it will take to hit the ground.
For this we have to put h = 0 and solve the quadratic.
Quadratic formula:
⇒ Standard equation : [tex]ax^2+bx+c=0[/tex]
⇒ [tex]x =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]
Now,
Solving the above equation with quadratic formula after comparing its values with the standard equation.
⇒ [tex]a=-16,\ b=24,\ c=1500[/tex]
⇒ [tex]t =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]
⇒ [tex]t =\frac{-24\pm \sqrt{(24)^2-4(-16)(1500)} }{2(-16)}[/tex]
⇒ [tex]t =\frac{-24\pm \sqrt{576+96,000} }{-32}[/tex]
⇒ [tex]t =\frac{-24\pm(310.76)}{-32}[/tex]
⇒ [tex]t =\frac{-24+(310.76)}{-32}[/tex] ⇒ [tex]t =\frac{-24-(310.76)}{-32}[/tex]
⇒ [tex]t =-\frac{286.76}{32}[/tex] ⇒ [tex]t =\frac{334.76}{32}[/tex]
⇒ [tex]t=-8.96\ sec[/tex] ⇒ [tex]t=10.46\ sec[/tex]
Discarding the negative values.
The pebble will hit the ground after 10.46 seconds.
Male African elephants have an average length of 7.5 meters. What is the combined average length, in centimeters, of five male African elephants?
Answer:
The combined average length of five male elephants is 3750cm
Step-by-step explanation:
1 elephant = 7.5m
5 elephants=?
We cross multiply.
5 * 7.5= 37.5m
So the average combined length of 5 male elephants is 37.5m
So we convert 37.5m to centimetres
Recall, 100cm = 1m
With this in mind, we convert 37.5m to cm by multiplying by 100
So, 37.5 x 100= 3750cm.
The combined average length of five male African elephants is 3750 centimeters, obtained by converting the length of one elephant to centimeters and multiplying by five.
Explanation:To calculate the combined average length, in centimeters, of five male African elephants, we start by converting the length of one elephant from meters to centimeters. Knowing that 1 meter is equivalent to 100 centimeters, we can find the length of one elephant in centimeters:
7.5 meters/elephant × 100 centimeters/meter = 750 centimeters/elephant
Now, to find the total length of five elephants:
750 centimeters/elephant × 5 elephants = 3750 centimeters
Therefore, the combined average length of five male African elephants is 3750 centimeters.
Consider a political discussion group consisting of 15 Democrats, 11 Republicans, and 8 Independents. 1. Find the number of three person subcommittees that can be made by choosing any republican, any democrat, and any independent. 2. Find the total number of possible 5 person subcommittees that can be chosen if the members can be any of the 34 people in the group. 3. Find the number of ways the Republicans can choose a subcommittee of 4 members. 4. Find the number of ways the Democrats can choose a subcommittee of 3 members. 5. Find the number of ways the Independents can choose a subcommittee of 3 members. 6. Find the number of ways the Independents can choose a Chairperson, Vice-chairperson, and Secretary, in this order. 7. Find the number of ways the Republicans can choose a Chairperson, Vice-chairperson, and Secretary, in this order. 8. Find the number of ways the Democrats can choose a Chairperson, Vice-chairperson, and Secretary, in this order.
Answer:
1) 1320 2)278256 3)330 4) 455 5)56 6)336 7) 990 8) 2730
Step-by-step explanation:
Solution:
1) Democrats = 15, Republicans = 11, Independents= 8
Total = 15+ 11+ 8 =34
Number of 3 persons committee = 15nCr 1 * 11nCr1 * 8nCr1
nCr =combination
Number of 3 persons committee that can be made by choosing any republican or democrat or independent = 15 * 11* 8 =1320
2)Total number of possible 5 person subcommittes from any 34 people = 34nCr5 = 34!/(29! * 5!)
=278256
3) Number of ways republicans choose subcomittee of 4 members = 11nCr4
= 11!/(7! * 4!)=330 ways
4) Number of ways democrats choose subcomittee of 3 members = 15nCr3
= 15!/ (12! *3!)=455 ways
5) Number of waysindependents choose subcomittee of 3 members = 8nCr3
= 8!/(5! * 3!)= 56 ways
6) Number of ways independents choose chairperson, vice chairperson and secretary:
As one picks each post the number of person decreases
= (Chairperson)* (vice chairperson) * (secretary) = 8nCr1 * 7nCr1 * 6nCr1
=336 ways
7) Number of ways republicans can choose chairperson, vice chairperson and secretary
As one picks each post the number of person decreases
= (Chairperson)* (vice chairperson) * (secretary) = 11nCr1 * 10nCr1 * 9nCr1
= 990ways
8) Number of ways Democrats can choose chairperson, vice chairperson and secretary
As one picks each post the number of person decreases
= (Chairperson)* (vice chairperson) * (secretary) = 15nCr1 * 14nCr1 * 13nCr1
= 2730 ways
Help me solve this out
What two products do you get when you cross-multiply the fractions 2/5 and 3/8?
a 10 and 12
b 6 and 40
c 16 and 15
d 3 and 5
When you cross-multiply the fractions 2/5 and 3/8, you obtain two products: 16 and 15.
Explanation:To find the products obtained when you cross-multiply the fractions 2/5 and 3/8, you multiply the numerator of the first fraction with the denominator of the second fraction, and the denominator of the first fraction with the numerator of the second fraction.
So, here are the steps:
Multiply 2 (numerator of the first fraction) by 8 (denominator of the second fraction). That gives you a product of 16. Multiply 5 (denominator of the first fraction) by 3 (numerator of the second fraction). That gives you a product of 15.
Therefore, the two products you get when you cross-multiply the fractions 2/5 and 3/8 are 16 and 15. Thus, the correct answer is option c: 16 and 15.
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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [a,b] into n equal subintervals and using the right-hand endpoint for each c Subscript k. Then take a limit of this sum as n right arrow infinity to calculate the area under the curve over [a,b]. f(x)equals4x over the interval [2,5]. Find a formula for the Riemann sum.
Answer with Step-by-step explanation:
We are given that
[tex]f(x)=4x[/tex]
Interval=[2,5]
[tex]h=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}[/tex]
[tex]x_i=i\frac{3}{n}[/tex]
Where i=1,2,3,... n
[tex]f(x_i)=4i\times \frac{3}{n}=\frac{12i}{n}[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\sum_{i=1}^{n}f(x_i)\cdot h=\lim_{n\rightarrow \infty}\sum_{i=1}^{n}(\frac{12i}{n}\times \frac{3}{n}[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{36}{n^2}\sum_{i=1}^{n}i[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{36}{n^2}\times \frac{n(n+1)}{2}[/tex]
By using
[tex]\sum n=\frac{n(n+1)}{2}[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{18n(n+1)}{n^2}=\lim_{n\rightarrow \infty}18(1+\frac{1}{n})[/tex]
Apply the limit
Area under the curve=[tex]18[/tex] square units
The Riemann sum formula for [tex]\(f(x) = 4x\)[/tex] over [2, 5] using right-hand endpoints and n subintervals is [tex]\(R_n = \sum_{k=1}^{n} 4\left(2 + k \cdot \frac{3}{n}\right) \cdot \frac{3}{n}\)[/tex]. The area is obtained by taking the limit as n approaches infinity.
The Riemann sum for a function f(x) over the interval [a, b] using right-hand endpoints and dividing the interval into n subintervals is given by:
[tex]\[ R_n = \sum_{k=1}^{n} f(c_k) \Delta x \][/tex]
where [tex]\( c_k \)[/tex] is the right-hand endpoint of the [tex]\( k \)[/tex]-th subinterval, [tex]\( \Delta x \)[/tex] is the width of each subinterval, and [tex]\( n \)[/tex] is the number of subintervals.
For the function f(x) = 4x over the interval [2, 5], the width of each subinterval [tex]\( \Delta x \)[/tex] is given by:
[tex]\[ \Delta x = \frac{b - a}{n} \][/tex]
In this case, [tex]\( a = 2 \), \( b = 5 \), and \( f(x) = 4x \)[/tex]. Therefore:
Now, the right-hand endpoint [tex]\( c_k \)[/tex] for each subinterval is given by:
[tex]\[ c_k = a + k \Delta x \][/tex]
Substitute the values:
[tex]\[ c_k = 2 + k \cdot \frac{3}{n} \][/tex]
[tex]\[ \Delta x = \frac{5 - 2}{n} = \frac{3}{n} \][/tex]
Now, substitute these expressions into the Riemann sum formula:
[tex]\[ R_n = \sum_{k=1}^{n} f(c_k) \Delta x \][/tex]
[tex]\[ R_n = \sum_{k=1}^{n} 4(2 + k \cdot \frac{3}{n}) \cdot \frac{3}{n} \][/tex]
Simplify this expression. To find the area under the curve, take the limit as n approaches infinity:
[tex]\[ \lim_{n \to \infty} R_n \][/tex]
This limit will give you the area under the curve f(x) = 4x over the interval [2, 5].
A researcher wants to test how much time stay at home dads do chores and housework compared to stay at home moms in one week. The study randomly selects 30 men and 30 women who are stay at home parents with one child and analyze their time spent doing housework and childcare in a week to find the average number of hours per week for each group.Which of the following should the researcher use to determine whether there is a difference in mean number of hours spent working as stay at home parents between men and women?a two-sample t-testb z-test for the population meanc paired t-testd ANOVA
Answer:
The correct option is;
a. two-sample t-test
Step-by-step explanation:
Here, since the test involves taking samples from two different population and then comparing parameters within the statistical results obtained from the samples, the appropriate statistical hypothesis testing to be used is the two sample t-test
A two sample t- test is used in statistical hypothesis testing on data from two samples obtained from different population so as to find out if the difference in the parameters of the two population are statistical significant.
Answer:
the answer is actually
Step-by-step explanation:
1. Start with 8 negative tiles
2.Separate the tiles into 2 equal groups
3. Count the number of tiles in each group.
absolute value of ___-2__ < __1.5___
Answer
the absolute value of -2 is greater than the absolute value of 1.5
Step-by-step explanation:
the absolute value of -2 is 2 and the absolute value of 1.5 is 1.5
The absolute value of -2 is 2, which is greater than 1.5. Therefore, this inequality is false.
The absolute value of -3.5 is 3.5, which is greater than 2.5. Therefore, this inequality is true.
From the information given, we have that;
|−2| < 1.5:
The absolute value of -2 is 2, which is greater than 1.5. Therefore, this inequality is false.
|−3.5| > 2.5:
The absolute value of -3.5 is 3.5, which is greater than 2.5. Therefore, this inequality is true.
Since we have an OR statement ("or"), if at least one of the inequalities is true, the entire statement is true.
In this case, only the second inequality is true.
Therefore, the overall statement is true.
The complete statement:
The absolute value ___-2__ < __1.5___ or ___-3.5 __ > _2.5______
21, 14, 18, 17, 27, 23, 25
mean, median, mode
Answer:
Mean: 20.714285714286 (rounds to 21)
Median: 21
Mode: No mode
Step-by-step explanation:
14 17 18 21 23 25 27
Mean:
14+17+18+21+23+25+27 = 145
145/7 = 20.7142857143
Median:
14 17 18 21 23 25 27
21 is in the middle of the numerical list
Mode:
None of the number repeat, so there is no mode.
The trend line passes through (10,9) and (35,0). Write an equation for the trend line.
The equation for the trend line that passes through the points (10,9) and (35,0) is calculated first by determining the slope, then the y-intercept. This results in the equation y = -0.36x + 12.6.
Explanation:
The subject matter of your question is in the realm of mathematics, specifically, the algebra of straight lines. Given the points (10,9) and (35,0) that a trend line passes through, the equation for this line can be determined using the slope and y-intercept.
First, let's compute the slope (m) which can be determined using the formula: m = (y2 - y1) / (x2 - x1). For our given points, this means: m = (0 - 9) / (35 - 10) = -9 / 25 = -0.36.
Next, we find the y-intercept (b) using the point-slope formula y - y1 = m (x - x1), substituting one of our points and the calculated slope: y - 9 = -0.36 (x - 10). Solving for y (y = -0.36x + b), we find: 9 = -0.36*10 + b which gives b = 9 + 3.6 = 12.6.
Therefore, the equation of the trend line, in the form of y = mx + b, is y = -0.36x + 12.6.
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Adam owns an inline skate shop. Adam wants to buy eight thousand four hundred fifty-eight inline skate wheels. Inline skate wheels sell in sets of four. A set of four skate wheels cost six dollars and forty-seven cents. How much money does Adam spend to buy eight thousand four hundred fifty-eight wheels? Adam puts eight wheels on every pair of inline skates. On how many pairs of inline skates can Adam put eight wheels? Between what two whole numbers is the number of pairs of inline skates Adam can put wheels on? Show all your mathematical thinking
Answer:
Cost: $13,680.82
Number of pairs of skates: 1057.25 / 1057-1058
Step-by-step explanation:
To find the cost of the wheels, we need to multiply the cost of a set, $6.47, by the number of wheels needed, 8458, for a quotient of 54723.26. We then divide this quotient by 4, the number of wheels in each set, to get the cost of $13,680.82.
Next, to find the number of pairs that Adam can put wheels on, we divide 8458, the number of wheels Adam has, by 8, the number of wheels Adam puts on each pair of skates. This leaves us with a quotient of 1057.25 pairs. The two whole numbers this number is between are 1057 and 1058.
Final answer:
Adam will spend $13,684.05 to purchase 2,115 sets of inline skate wheels.
He can put eight wheels on 1,057 pairs of inline skates, and the number falls between 1,057 and 1,058 pairs.
Explanation:
The student asked how much money Adam would spend to buy eight thousand four hundred fifty-eight inline skate wheels, given that skate wheels are sold in sets of four and each set cost six dollars and forty-seven cents. To find the total cost, we need to determine how many sets of four wheels are needed and then multiply by the cost per set.
First, we'll calculate the number of sets by dividing the total number of wheels by the number of wheels in a set:
Number of sets = Total wheels / Wheels in a setNumber of sets = 8,458 / 4Number of sets = 2,114.5Since you can't buy half a set, Adam needs to buy 2,115 sets of wheels.
Next, we multiply the number of sets by the cost per set to find the total cost:
Total cost = Number of sets × Cost per setTotal cost = 2,115 × $6.47Total cost = $13,684.05To determine how many pairs of inline skates Adam can equip with eight wheels, we divide the total number of wheels by eight:
Number of pairs = Total wheels / Wheels per pairNumber of pairs = 8,458 / 8Number of pairs = 1,057.25Adam can fully equip 1,057 pairs of inline skates with eight wheels, since you can't have a quarter of a pair of skates. Therefore, the number of pairs of inline skates Adam can put wheels on falls between 1,057 and 1,058.
Use the distributive property
Answer:
Step-by-step explanation:
Using the distributive property of multiplication
3( 4x - 9)
= 12x - 27
Answer:
12x - 27
Step-by-step explanation:
multiply the 3 to both 4x and -9
3 * 4x = 12x
3 * -9 = -27
combine
12x - 27
Given that a randomly chosen customer like cakes what is the probability that the customer also likes pie
Answer:
1/2 because cake are almost made out of the same thing pie are made of so they are using half of the intransigents to make cake and there using it to make pie
Step-by-step explanation:
Answer:
A. 2/7
Step-by-step explanation:
took the test on edg.2020
good luck :)
$65 × 25%
$823×21.4%
$33,333×4.3%
$12,831×52%
$44,893×3.4%
$65×25%=$65×($65×0.25)=$1056.25
$823×21.4%=$823×($823×0.214)=$144,948.406
$33,333×4.3%=$33,333×($33,333×0.043)=$47,776,822.227
$12,831×52%=$12,831×($12,831×0.52)=$85,609,971.72
$44,893×3.4%=44,893×(44,893×0,034)=$68,522,969.266
Evaluate 9 – b when b = 8 what’s
the answer
Answer:
1
Step-by-step explanation:
9-b is the same as 9-8 because b=8. 9-8=1.
1) A chemist has 250 ml of a 5% acid solution. How much water should be added to this solution to reduce it to a 3% solution.
Answer:
153.1ml
Step-by-step explanation:
We have 12.5ml of acid in the solution.
If we want this to be 3% then we can divide this value by 3 and times by 100 to get the total value.
416.6ml total solution amount
415.6-12.5-250=153.1
14. Sarah bought a lawnmower for $320. She signed up for the buy now pay later plan at the store with the following conditions: $100
down and payments of $25 for the next 12 months. The extra cost paid by taking this plan is equivalent to what actual yearly rate of
interest?
A. 85%
B. 65%
CC. 67%
D. 25%
Answer:
D
Step-by-step explanation:
100+25 * 12 ; 100+300 = 400 ; difference = 400-320=80 ; percent increase since it is 1 year = 80/320 =1/4=0.25 = 25/100=25%
What is the nth term rule of the quadratic sequence below?
-4, -3, 0, 5, 12, 21, 32
Answer:
The nth term = n^2 - 2n - 3.
Step-by-step explanation:
-4 -3 0 5 12 21 32
Differences 1 3 5 7 9 11
Difference 2 2 2 2 2 <-- divide this by 2 so its n^2.
So the first term is n^2
List the original numbers and values of n^2:
sequence -4 -3 0 5 12 21 32
n^2 1 4 9 16 25 36 49
Subtract -5 -7 -9 -11 -13 -15 -17
These last numbers have a common difference of -2 so the next part of the answer is -2n and get the -5, -7 etc we add -3.
So our formula is n^2 - 2n - 3.
Check for the 3rd term:
3rd term is 3^2 - 2(3) - 3 = 0.
5th term = 5^2 - 2(5) - 3 = 25 - 10 - 3 = 12.
If a block of copper is 5 cm by 10 cm by 3 cm and has a mass of 1335 grams, what is the density of copper?
Answer:
the density of copper is 90.03g/cm³
Step-by-step explanation:
This problem bothers on the density of a substance, this case for a copper material
Given data
Mass of copper m = 1355g
Volume of copper block v= l*b*h
10*5*3=150cm³
We know that the density
ρ= mass/volume
ρ= 1355/150
ρ= 90.03g/cm²
The density of a substance is defined as the mass of the substance per unit volume
Answer:
The answer is 8.9 gm/cm cubed
Step-by-step explanation:
Just did it on algebra nation
The box plots show Lauren's chemistry scores and her biology scores. Chemistry 2 box plots. The number line goes from 50 to 100. For chemistry, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80. For biology, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70. Biology Lauren used the steps below to determine the differences in the medians and the interquartile ranges.
Answer:
D
Step-by-step explanation:
Just did the test
The error is in ''Step 3.''
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The box plots show Lauren's chemistry scores and her biology scores.
Now,
She should have calculated the interquartile range as,
Chemistry = 85 - 60 = 25
Biology = 80 - 60 = 20
In a box plot, The median is the point on the number line where a line divides the rectangular box.
Thus, from the information given in the question about the box plots, the median for Chemistry = 80 (this is where a line divides the box)
Median for Biology = 70
The difference in the median = 80 - 70 = 10.
Lauren didn't make any mistake in Step 1 and 2, as he equally got the same values.
⇒ The interquartile range in a box plot is simply the difference in the ranges = (Q3 - Q1).
From the given information,
The interquartile range for Chemistry = 85 - 60
= 25
And, The Interquartile range for Biology = 80 - 60
= 20
The difference in interquartile range = 25 - 20 = 5
Therefore, Lauren made an error in ''Step 3'' when calculating the interquartile range for both Chemistry and Biology, even though he arrive at the same value of the difference in the interquartile range we got as calculated above.
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The complete question is this,
The box plots show Lauren's chemistry scores and her biology scores. Chemistry 2 box plots. The number line goes from 50 to 100. For chemistry, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80. For biology, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70. Biology Lauren used the steps below to determine the differences in the medians and the interquartile ranges. Step 1 Find the median for chemistry: 80 Find the median for biology: 70 Step 2 Find the difference in the medians: 80 minus 70 = 10 Step 3 Find the interquartile range for chemistry: 85 minus 80 = 5 Find the interquartile range for biology: 80 minus 70 = 10 Step 4 Find the difference in the interquartile ranges: 10 minus 5 = 5 Lauren determined that the difference in the medians is greater than the difference in the interquartile ranges. Which explains Lauren's error?
Describe a probability simulation for each situation
1. You guess the answers on a true/false test with 20 questions
2. One student out of 6 is randomly chosen to be the homeroom representative
Simulate a true/false test by flipping a coin for each question with heads for 'true' and tails for 'false'. To select a homeroom representative from six students, assign numbers and use a random number generator or equivalent method for random selection.
To simulate the situation where you guess the answers on a true/false test with 20 questions, you could use a coin to represent the random guessing. Flip the coin 20 times where heads represents 'true' and tails represents 'false', recording the number of correct outcomes as needed. Since each question can only have one correct answer, the probability of getting a question right is 0.50.
For the situation where one student out of 6 is randomly chosen to be the homeroom representative, you could assign each of the six students a number from 1 to 6. Then, using a random number generator, die, or drawing numbers from a hat, you select a number at random to determine the representative. The probability of any one student being selected is [tex]\frac{1}{6}[/tex] or approximately 0.17.
A culture of bacteria has an initial population of 8300 bacteria and doubles every 10 hours. Using the formula Pt=P0*2^t/d , where Pt is the population after t hours, P0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 3 hours, to the nearest whole number?
Answer:
10,219 bacteria
Step-by-step explanation:
In this question, we are asked to calculate the population of bacteria in a culture given the formula for the population increase.
From the question, we know the formula to use is
Pt=Po*2^t/d
From the parameters in the question, we identify that Pt is ?, Po is 8300 bacteria , t is 3 hours and d is 10 hours which is the doubling time. Inserting these figures we have;
Pt = 8300 * 2^(3/10)
Pt = 8300 * 2^0.3
Pt = 10,218.5
Pt = 10,219 bacteria to the nearest whole number
Answer:
10218
Step-by-step explanation:
A culture of bacteria has an initial population of 8300 bacteria and doubles every 10 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P
t
=P
0
⋅2
d
t
, where P_tP
t
is the population after t hours, P_0P
0
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 3 hours, to the nearest whole number?
P_0=8300
P
0
=8300
The initial population
t=3
t=3
Time elapsed
d=10
d=10
The doubling time
P_t = P_0\cdot 2^{\frac{t}{d}}
P
t
=P
0
⋅2
d
t
P_t=8300\cdot 2^\frac{3}{10}
P
t
=8300⋅2
10
3
Plug in
P_t=10218.4986\approx10218
P
t
=10218.4986≈10218
Use parenthesis in the calculator for the exponent
10218
What is the measure of the missing angle in this triangle?
Answer:
Its 25°Explanation:
Its The Smallest Angle Thats There Because If It Was 60° Or 150° They Would Be Bigger And If It Was 35° It Would Be The Same As The Other Angle 35°The measure of the missing angle is [tex]25^\circ[/tex]. So, the first option is correct.
Important information:
Measure of the first angle is 35 degrees.Measure of the second angle is 120 degrees.We need to find the third angle of the triangle.
Angle sum property:According to the angle sum property, the sum measure of all interior angles of a triangle is 180 degrees.
Let [tex]x[/tex] be the measure of the missing angle.
[tex]x+35^\circ+120^\circ=180^\circ[/tex]
[tex]x+155^\circ=180^\circ[/tex]
[tex]x=180^\circ-155^\circ[/tex]
[tex]x=25^\circ[/tex]
Thus, the first option is correct.
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an angle is a..... if the vertex is on a circle and the sides of the angle are chords of the the circle
Answer:
Inscribed angle
Step-by-step explanation:
an angle is a inscribed angle if the vertex is on a circle and the sides of the angle are chords of the the circle
Final answer:
An angle with its vertex on a circle and sides that are chords of the circle is called an inscribed angle. This concept relates to the angle of rotation, which is the arc length divided by the radius of the circle.
Explanation:
An angle with its vertex on a circle and sides that are chords of the circle is known as an inscribed angle. The angle is formed by the two chords that intersect on the circumference of the circle, creating an angle inside the circle.
To understand this concept in relation to movement along a circle's circumference, like a compact disc (CD), one can think of the movement in terms of the angle of rotation. For any point on a rotating CD, the rotation angle can be calculated. This angle is the ratio of the arc length (the distance traveled along the circumference) to the radius of the circle. If the CD completes one full revolution, this angle equals 2π radians (or 360 degrees), indicating a full rotation.
Understanding inscribed angles and rotation angles helps us think about geometric figures and rotational movement, whether in a mathematical problem or in a physical example like a CD rotating on its axis.
An element with a mass of 630 grams decays by 30% per minute. To the nearest minute, how long will it be untill there are 30 grams of the element remaining?
Answer:
It should take somewhere between 8 to 9 minutes to decay until there are 30 grams remaining.
It will take about 8 minutes until there are 30 grams of the element remaining.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
we can use the formula for exponential decay:
[tex]N(t) = N_{0} e^(^-^k^t^)[/tex]
where:
N₀ is the initial quantity (in grams) of the element
N(t) is the quantity (in grams) of the element at time t
k is the decay constant
t is the time (in minutes)
We can start by finding the value of k, which is related to the percentage of decay per minute:
k = ln(1 - %/100)
= ln(1 - 30/100)
= -0.35667
Next, we can plug in the values we have and solve for t:
[tex]30 = 630.e^(^-^0^.^3^5^6^6^7^t^)[/tex]
Dividing both sides by 630, we get:
[tex]0.0476 = e^(^-^0^.^3^5^6^6^7^t^)[/tex]
Taking the natural logarithm of both sides, we get:
ln(0.0476) = -0.35667t
Solving for t, we get:
t = 7.75
Therefore, it will take about 8 minutes until there are 30 grams of the element remaining.
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Solve the system 2/3x-1/2y=1
1/4x+3/4y=-1
Answer:
y=4x/3-2 x=-3y-4
Step-by-step explanation:
kerry cut an 8 foot long board 6 pieces that are equal in length
Answer:
1 1/3 ft
Step-by-step explanation:
We have 8 feet of board to work with. In order to find how long each of the 6 pieces are, we need to divide 8 by 6: 8 / 6 = 4 / 3 = 1 1/3 ft.
Thus, the length of each piece is 1 1/3 ft.
Hope this helps!
Archimedes knew that at 7 AM, the sunlight reaches the ground at an angle of 31, degrees. The rock beside which he slept was 5 meters tall.How far from the rock did Archimedes go to sleep?Round your final answer to the nearest hundredth. *
Answer: Archimedes go to sleep at 8.32 metres away from the rock.
Step-by-step explanation:
Given that the rock beside which he slept was 5 meters tall
Height h = 5m
Angle Ø = 31 degree
To get distance x away from the rock, we will use trigonometry function. SohCahToa
TanØ = opposite/adjacent
Tan 31 = 5/x
x = 5/tan31
x = 8.32m
To find the distance from the rock where Archimedes went to sleep, we calculate the adjacent side of a right triangle using the tangent function with the given angle of 31 degrees and the rock's height of 5 meters. The result is approximately 8.32 meters.
The student's question involves finding the distance from the rock where Archimedes slept to the point where the sunlight hit the ground at a 31-degree angle.
This scenario forms a right triangle with the rock's height as the opposite side, the distance from the rock as the adjacent side, and the Sun's angle providing information to use trigonometry—specifically, the tangent function since we have the opposite side and are looking for the adjacent side.
To calculate the distance, we use the equation tan(angle) = opposite/adjacent, which can be transformed into adjacent = opposite/tan(angle).
Plugging in the values, we get:
adjacent = 5 meters/tan(31 degrees)
adjacent = 8.32
We find that the adjacent side, which is the distance from the rock, is approximately 8.32 meters.
Therefore, Archimedes went to sleep roughly 8.32 meters away from the rock.
A board is leaning against a vertical wall. One end of the board rests on the ground at a point eight feet from the wall. The other end of the board touches the wall at a point that is six feet above the ground.
35 POINTS!Use a trigonometric function to determine the angle that the board creates with the ground (m∠A). In at least four sentences, explain why you chose your specific function and how it applies to the measure of angle A. Be sure to include the key vocabulary words "tangent", "ratio", "opposite side", "adjacent side" and "angle measure" in your response. Describe each computational step in complete sentences.
Answer:
36.87°
Step-by-step explanation:
Since ABC is a right-angle triangle, we can use trigonometric ratios to solve for unknown angles and sides.
For Angle at A, we have lengths of opposite and adjacent sides so we can use tangent at A.
tan(A) = opposite/adjacent
tan(A) = CB/AB
tan(A) = 6/8
A = (tan^-1)(0.75)
A = 36.86989765°
Three students are playing a game using the spinner above. Each student draws three boxes on a piece of paper. The spinner is spun, and each student writes the number in any one of the three boxes. The spinner is spun two more times, and each time the students write the number in a remaining empty box. The students then compare numbers, and whoever has the largest three-digit number wins the game.This game would be particularly useful in helping students' understanding of:
Answer:
Probability
Step-by-step explanation:
In this game, the players rely entirely on chance to win, rather than skill. Therefore, this game would be particularly useful in helping students' understanding of probability.
(Spoken from someone who played this exact game 2 years ago to learn about probability.)
An order is received for 400 loaves of whole wheat bread, 200 loaves of oat bread, and 350 loaves of rye bread. Given that the cost of mixing, baking, and packaging is $14, $25, and$2, respectively, per hour, find matrices B and C so that the product BAC will give the total cost (excluding raw materials) of filling this order. Find the total cost.
The total cost (excluding raw materials) of filling this order is $11,300.
Let's denote the matrices as follows:
[tex]\[ B = \begin{bmatrix} 400 \\ 200 \\ 350 \end{bmatrix} \][/tex]
This matrix represents the number of loaves for each type of bread.
[tex]\[ A = \begin{bmatrix} 14 & 25 & 2 \end{bmatrix} \][/tex]
This matrix represents the cost per hour for mixing, baking, and packaging.
[tex]\[ C = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \][/tex]
This matrix represents the number of hours needed for each process (mixing, baking, packaging).
Now, we can calculate the product BAC to find the total cost:
[tex]\[ BAC = B \cdot A \cdot C \][/tex]
Let's perform the calculations:
[tex]\[ BAC = \begin{bmatrix} 400 \\ 200 \\ 350 \end{bmatrix} \begin{bmatrix} 14 & 25 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \][/tex]
[tex]\[ BAC = \begin{bmatrix} (400 \times 14 + 200 \times 25 + 350 \times 2) \end{bmatrix} \][/tex]
[tex]\[ BAC = \begin{bmatrix} 5600 + 5000 + 700 \end{bmatrix} \][/tex]
[tex]\[ BAC = \begin{bmatrix} 11300 \end{bmatrix} \][/tex]
So, the total cost (excluding raw materials) of filling this order is $11,300.