Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.
Answer:
Maliks
Step-by-step explanation:
Round this number to the
nearest ten:
801
Answer:
800
Step-by-step explanation:
the answer is 800 as 1 rounds down
What does it mean to construct a triangle inscribed in a circle? (what does the word inscribed mean?)
Answer: A geometric figure which touches only the sides (or interior) of another figure.
Step-by-step explanation:
its inside but does not go past the innner edges
i need help with thiss
The only true statement in the following equation are B and D.
How to find true statement?A. When the bacteria population reaches 900, 12 hours have passed since the colony was placed on the petri dish.
To check this statement, we can use the formula for exponential growth:
P(t) = P0 * [tex]3^{(t/6)[/tex]
Where P(t) is the population at time t, P0 is the initial population, and t is the time in hours.
If P(t) = 900, we can solve for t:
900 = [tex]100 * 3^{(t/6)[/tex]
9 = [tex]3^{(t/6)[/tex]
ln(9) = (t/6) * ln(3)
t = 6 * ln(9) / ln(3) ≈ 12.68
So, it takes approximately 12.68 hours for the population to reach 900. Therefore, statement A is false.
B. Three hours after the colony is placed on the petri dish, there are 200 bacteria.
Using the formula above with t=3:
P(3) = [tex]100 * 3^{(3/6) = 200[/tex]
So, statement B is true.
C. Three hours after the colony is placed on the petri dish, there are about 173 bacteria in the colony.
Using the formula above with t=3:
P(3) = [tex]100 * 3^{(3/6) = 200[/tex]
So, statement C is false.
D. In the first hour the colony is placed on the petri dish, the population grows by a factor of [tex]$3^{\frac{1}{6}}$[/tex]
Using the formula above with t=1:
P(1) = [tex]100 * 3^(1/6)[/tex]
So, the population after 1 hour is 100 times the sixth root of 3. We can write this as:
P(1) = [tex]100 * (3^(1/6)) = 100 * 3^{\frac{1}{6}}[/tex]
Therefore, statement D is true.
E. Between 8 a.m. and 9 a.m., the population grows by a factor of [tex]$3^{\frac{2}{3}}$[/tex]
Between 7 a.m. and 8 a.m., the population grows by a factor of 3. Then, between 8 a.m. and 9 a.m., it grows by another factor of 3. So, between 7 a.m. and 9 a.m., the population grows by a factor of [tex]3^2[/tex] = 9. Taking the sixth root of 9 gives:
[tex](3^2)^(1/6) = 3^(1/3) = 3^{\frac{2}{6}} = 3^{\frac{1}{3}}[/tex]
So, the population between 8 a.m. and 9 a.m. grows by a factor of [tex]3^(1/3)[/tex]. Therefore, statement E is false.
In summary, the true statements are B and D.
We can employ the AC approach to factor the quadratic expression seen in the image. To achieve -6 * -15 = 90, we first multiply the coefficients of the first and last terms. The middle term's coefficient, which is -9, is then shown to be two factors of 90. Since -6 * -15 = 90 and -6 + (-15) = -21, which is the same as -9 when we factor out the GCF of 3, these factors are -6 and -15:
[tex]x^2 - 9x - 90 = (x - 15)(x + 6)[/tex]
As a result, the quadratic expression's factored form is (x - 15)(x + 6).
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A certain company's main source of income is selling socks.
The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by:
P(x)=−3(x−5) ^2+12
What is the maximum profit that the company can earn?
____ million dollars
If the company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by P(x)=−3(x−5) ^2+12, the maximum profit is $87 million.
The given profit function is in the form of a quadratic equation with a negative coefficient of the squared term. This means that the graph of the function is a downward-facing parabola, and the vertex of this parabola represents the maximum value of the function.
To find the vertex, we need to convert the given function into vertex form:
P(x) = -3(x - 5)^2 + 12
= -3(x^2 - 10x + 25) + 12
= -3x^2 + 30x - 63
Completing the square, we get:
P(x) = -3(x - 5)^2 + 12 + 75
= -3(x - 5)^2 + 87
The vertex of this parabola is at the point (5, 87), which represents the maximum profit the company can earn.
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what is the value of the expression 9 (5) - X / Y when x= 15 and y= 3
a 5
b 10
c 15
d 20
Answer:
9(5)-/y
9(5)-15/3
45-15/3
45-5
40
To make cherry trail mix, Sebastián needs 4 oz of nuts for every 3 oz of dried cherries. To make sunflower trail mix, he needs 5 oz of nuts for every 2 oz of sunflower seeds. Can Sebastian make more cherry trail mix or sunflower trail mix with 20 oz of nuts? Show your work.
Answer:
Cherry Trail Mix
Step-by-step explanation:
cherry trail mix ratio = 4:3
sunflower trail mix ration = 5:2
4 goes into 20 5 times so multiply 3 by 5 to get 15. Add them together to make 35 oz
5 goes into 20 4 times so multiply w by 4 to get 8. Add them together to make 28 oz
35 > 28
prove that (sec theta + tan theta - 1)(sec theta - tan theta + 1) = 2tan theta
Answer:
(secΘ+tanΘ-1)(secΘ-tanΘ+1)
=sec²Θ-secΘtanΘ+secΘ+secΘtan-tan²Θ+tanΘ-secΘ+tanΘ-1
=2tanΘ+(sec²Θ-tan²Θ)-1
=2tanΘ+1-1
=2tanΘ
The explicit formula of an arithmetic sequence is an=−6−4(n−1). What is the recursive formula of the sequence? ( 1 point)
A. an+1=an−4, a1=−6
B.an+1=an−6, a1=−4
C. an+1=an+4, a1=−6
D. an+1=an−4
Answer: Option A. an+1=an-4, a1=-6
Step-by-step explanation:
Please answer the both questions in the photos below ( will mark brainliest if available + 30p )
Answer:
(5,1)
(7, -5)
Step-by-step explanation:
y = mx + b
The b is the y intercept. This is where the graph crosses the y axis. Graph this first. The m is the slope. It is the rise over the run. You can make any number a fraction by putting it over 1. From the y-intercept you use the slope (rise/run) to graph the second point.
For example, if the slope is 1. then 1/1 would show your rise and run. Start when the y-intercept is and go up 1 and then 1 right. Connect the two points that you have graphed.
If the slope is 2/7, then from the y-intercept go up 2 and right 7. Graph that point and draw a line connecting that point to the point on the y-intercept.
Helping in the name of Jesus.
ANSWER OF THE FIRST TWO EQUATIONS
y = x -4
y= -x+6
both the equations represent a straight line with y intercept as -4 and 6 respectively
x-y-4 = 0. ........(equation 1)
x+y-6 = 0. .........(equation 2)
adding equation 1 and 2
2x - 10 = 0
x = 5
subtracting equation 2 from 1
-2y -2 = 0
y = 1
FINAL ANS : (5,1)
Sean throws the discus at a school meet and the height of the discus is given by the function h=-16+2 + 38t + 5, where h is in feet and t represents the seconds after throwing. A. What is the initial height of the discus? b. After how many seconds does it take for the discus hit the ground?
Hence, in response to the provided question, we can say that As a result, function the discus takes approximately 0.03125 seconds to strike the ground.
what is function?Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.
The supplied function for discus height is as follows:
[tex]h(t) = -16t^2 + 38t + 5\\h(0) = -16(0)^2 + 38(0) + 5 = 5[/tex]
As a result, the discus's starting height is 5 feet.
[tex]-16t^2 + 38t + 5 = 0\\[/tex]
To find t, we can apply the quadratic formula:
t = (-b \sqrt(b2 - 4ac)) (2a)
where a=-16, b=38, and c=5.
[tex]t = (-38 + \sqrt(38^2 - 4(-16)(5))) / (2(-16))\\t = (-38 + \sqrt(1524)) / (-32) (-32)\\t = (-38 + 39) / (-32) (-32)\\[/tex]
As a result, [tex]t = (-38 + 39) / (32) or t = (-38 - 39) / (32) (-32)[/tex]
t = 1/32 or t = 77/32
As the negative value doesn't make sense in this situation, we chose the positive value:
t = 1/32
As a result, the discus takes approximately 0.03125 seconds to strike the ground.
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Identify the function in standard form. 3x 2 + 6x - 12 = 0 3x 2 + 2x + 10 = 0 5x 2 - 10x + 5 = 0 2x 2 - 4x + 6 = 0
All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:
ax² + bx + c = 0.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x² is a prerequisite for an equation to be a quadratic equation.
The functions in standard form are:
3x² + 6x - 12 = 0
3x² + 2x + 10 = 0
5x² - 10x + 5 = 0
2x² - 4x + 6 = 0
All of these equations are quadratic equations in standard form, where the highest power of x is 2. The standard form of a quadratic equation is:
ax² + bx + c = 0
where a, b, and c are constants and a ≠ 0.
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i need help please help me
According the question given above the value of n is 21.
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
Calculations and problem-solving techniques simplify the issue. The act of substituting a complex mathematical expression with a simpler counterpart is known as simplification (usually shorter).
Here, we have
Given : 7 = n/3
we have to find the value οf n.
We apply simplification here and we get
7 = n/3
n = 7×3
n = 21.
Hence, the value οf n is 21.
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The ordered pair (a,b) satisfies the inequality y
Answer:
If you add 5 to a, it will be greater than b
Step-by-step explanation:
i got it right
a model rocket is 5cm tall. If it was built with a scale of 1cm: 2m, then how tall is the real rocket?
Answer:
If the model is 5cm and 1cm is equal to 2m, it means the actual rocket is 10 meters.
Step-by-step explanation:
1cm = 2m
5cm is 5 times the amount of 1cm.
10m is 5 times the amount of 2m
Answer : 10 Meters
Explanation : 2 × 5 = 10
According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that .
a. Find the probability that at least 29% of the sample are from poverty-level households, assuming that 22% of all children under the age of 6 in this state live in poverty-level households.
b. Based on your answer to part (a), is there convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%? Explain your reasoning.
a. The resultant probability is 0.17%
b. The resultant statement greater than the national value of 22% is true.
The probability that at least 29% of the sample are from poverty-level households is 0.17% and we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.
According to government data, 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children from one state and finds that at least 29% of the sample are from poverty-level households.
To answer part (a) of the question, we can use the normal approximation to the binomial distribution. The mean of the distribution is np = 300 * 0.22 = 66 and the standard deviation is sqrt(np(1-p)) = sqrt(66 * 0.78) = 7.09. We can use the normalcdf function to find the probability that at least 29% of the sample are from poverty-level households:
normalcdf(87.5, 300, 66, 7.09) = 0.0017
So the probability is 0.17%.
For part (b) of the question, we need to determine if there is convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.
Since the probability that at least 29% of the sample are from poverty-level households is 0.17%, which is very small, we can conclude that there is not convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.
The small probability suggests that the observed sample result is unlikely to occur by chance if the true population proportion is 22%, so we do not have enough evidence to reject the null hypothesis that the population proportion is equal to 22%.
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Q26) Suppose you are a project manager, and you estimate that the time it takes to complete a particular task on your project follows a normal distribution with a mean of 20 days and a standard deviation of 3 days. What is the probability that the task will take more than 25 days to complete?
The probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.
To find the probability of a task taking more than 25 days to complete, given that the mean and standard deviation of the normal distribution are 20 and 3 days, respectively, one can use the Z-score formula.Z = (X - μ)/σwhere Z is the standard score, X is the observed value, μ is the mean, and σ is the standard deviation. Therefore,Z = (25 - 20)/3 = 5/3 ≈ 1.67The area to the right of Z = 1.67 on a standard normal distribution table represents the probability that the task will take more than 25 days to complete. Using a standard normal distribution table or calculator, we can find that P(Z > 1.67) = 0.0475 or approximately 4.75%.Therefore, the probability that the task will take more than 25 days to complete is 0.0475 or approximately 4.75%.
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What is the monthly periodic rate on a loan with an APR of 20.3%
The monthly periodic rate with APR 20.3% is 1.69%
What is APR?APR is also known as Annual Payment Rate. And it is the cost of your mortgage credit as a yearly rate.
Annual Percentage Rate is typically higher than your interest rate because it includes your interest rate plus certain fees, such as lender and mortgage broker fees, based on the specific characteristics of your loan.
Monthly Interest Payment means the amount of interest paid on a Payment Date for the preceding Interest Period based on interest calculated for such preceding Interest Period at the Monthly Interest Rate.
If the Annual Percentage Rate is 20.3% and there are 12 months on a year , the monthly interest = 20.3/12 = 1.69 %
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A population of 250 wild turkeys decreases by 2. 2% per year. At the end of 8 years, there will be approximately 209 turkeys in the population. Which function can be used to determine the number of turkeys, y, in this population at the end of t years?
We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878. The number of turkeys, y, in the population at the end of t years is obtained by substituting this value into the exponential decay formula and getting the following result: y = 250(0.878)t.
The equation y = 250(1 - 0.022)t, where t is the number of years, may be used to calculate the number of turkeys, y, in this population at the end of t years.
Using the exponential decay formula, A = P(1 - r)t, where A is the final amount, P is the beginning amount, r is the rate of decay in decimal notation, and t is the duration in years, we may arrive at this function.
If we substitute the values provided, we get: 209 = 250(1 - 0.022)^8
We may calculate (1 - 0.022)8 as (1 - 0.022)8 = 0.878.
This value may be substituted into the exponential decay formula to obtain the number of turkeys, y, in the population at the end of t years: y = 250(0.878)t.
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what is this question for math need help
Answer:
A
Step-by-step explanation:
The answer is 2x+2y+2 which is A
Answer: I think its B but I'm not quite sure
Step-by-step explanation:
please help
30 points
The baker can decorate 1.4 or 1 1/3 of cupcakes in a minute.Step-by-step explanation: 42 cupcakes in 30 minutes so if you divide 42 cupcakes in 30 groups you get 1 in each group and 12 left so if make 30 in 3 it makes 4 in each group but it is 30 so you make the four in to a 0.4 or 1/3 which is 1.4.You can also multiply if you make 1.4 into 14 x 3 = 42 same as 1.4 x 30 = 42 so the answer is 1.4.
There are 9 teams that are numbered respectively from 1 to 9. Each team member has the group number printed on his/her shirt and each team cannot have more team members then its number. Armen started to add up all the odd numbers he saw on the shirts and asked David to add up all the even ones. What is the greatest possible difference between David's results and Armen's
The greatest possible difference between David's result and Armen's result is 5.
Let's first consider the maximum number of odd shirts Armen can count. Since there are only 5 odd numbers between 1 and 9, the maximum number of odd shirts Armen can count is 1+3+5+7+9 = 25.
Now, let's consider the maximum number of even shirts David can count. Since there are only 4 even numbers between 1 and 9, the maximum number of even shirts David can count is 2+4+6+8 = 20.
Therefore, the greatest possible difference between David's result and Armen's result is
= 25 - 20
Subtract the numbers
= 5
The maximum difference occurs when Armen counts all 5 odd shirts and David counts all 4 even shirts.
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Use the Pythagorean identity, (a²- y2)2 + (2xy)² = (x² + y²)2, to create a Pythagorean triple.
Follow these steps:
1. Choose two numbers and identify which is replacing and which is replacing y.
2. How did you know which number to use for x and for y
3. Explain how to find a Pythagorean triple using those numbers.
4. Explain why at least one leg of the triangle that the Pythagorean triple represents must have an even-numbered length.
The Pythagorean triple created by the steps are (3, 4, 5) where the hypotenuse is 5
How to create a Pythagorean triple.The numbers x and y
Let's choose 3 and 4 as our x and y, respectively.
How we chose x and y
We can choose any numbers for x and y.
However, we usually choose numbers such that x > y to avoid duplicates.
Finding the triple
To find the Pythagorean triple, we substitute x = 3 and y = 4 in the Pythagorean identity:
(x²- y²)² + (2xy)² = (x² + y²)²
(3² - 4²)² + (2(3)(4))² = (3² + 4²)²
(-7)² + (24)² = (9)² + (16)²
49 + 576 = 81 + 256
625 = 625
We can see that this equation is true, which means that (3, 4, 5) is a Pythagorean triple.
Why at least one leg must be even
At least one leg of the triangle represented by the Pythagorean triple must have an even-numbered length because if one of the legs is odd, then the other leg and the hypotenuse must be odd too.
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Mr. Shoaf had a birthday a couple weeks ago and his mom took him out to dinner.
The total bill was $76.55. If there was a 5% sales tax and she tipped 25%, what was the total Mr. Shoaf’s mom paid for dinner?
She paid---------------------------------- dollars for the birthday dinner.
The birthday supper cost $94.73 and also the tax rate is $72.72 and was paid by Mr. Shoaf's mother.
What distinguishes VAT from sales tax?A flat charge called valuation tax (VAT) is imposed on a purchase. It resembles a sales tax in the some ways, but unlike with a state taxes, the consumer pays the entire amount due to the government at the moment of sale.
What does Dutch VAT mean?Value added tax is levied by the Dutch government on all products and services. VAT is added by businesses to the sales price to determine the final amount that customers pay. Businesses must pay taxes to the Customs and Tax Administration when goods are sold.
Cost of the meal [tex]= 76.55 -[/tex] (5% of 76.55)
Cost of the meal [tex]= 76.55 - 3.83[/tex]
Cost of the meal [tex]= 72.72[/tex]
calculate tip,
Tip = 25% of the cost of the meal
Tip [tex]= 0.25 *72.72[/tex]
Tip [tex]= 18.18[/tex]
calculate the total amount paid
Total amount paid = cost of the meal + sales tax + tip
Total amount paid [tex]= 72.72 + 3.83 + 18.18[/tex]
Total amount paid [tex]= 94.73[/tex]
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The area of a triangle is one fourth the area of a square. If the base of the triangle and a
side of the square are equal, what is the ratio of the side of the square to the height of the
triangle?
Answer:
see below
Step-by-step explanation:
2:1
Look at the image below.
He amount of soda in a 12 ounce bottle is supposed to be 12 ounces, right? There is some variability in the amount that the machines dispense into the bottles. Let the real amount of soda in each bottle follow a Normal distribution with mean 12. 2 and standard deviation 0. 3.
If the bottle can only hold 13 ounces, what is the probability the bottle will overflow?
(In other words, what is the probability that the machine dispenses more than 13 ounces?)
If the bottle can only hold 13 ounces, then the probability the bottle will overflow is approximately 0.0032 or 0.32%.
First, we need to calculate the z-score, which is the number of standard deviations that the mean value of 12.2 ounces is away from the bottle's capacity of 13 ounces. We can calculate the z-score using the formula:
z = (x - μ) / σ
where x is the bottle capacity (13 ounces), μ is the mean value of soda dispensed by the machine (12.2 ounces), and σ is the standard deviation (0.3 ounces).
Substituting the values, we get:
z = (13 - 12.2) / 0.3 = 2.67
The z-score of 2.67 means that the bottle capacity of 13 ounces is 2.67 standard deviations away from the mean value of soda dispensed by the machine.
Substituting the values, we get:
P(Z > 2.67) = 1 - P(Z ≤ 2.67) = 1 - 0.9968 = 0.0032
Therefore, the probability of the soda bottle overflowing is approximately 0.0032 or 0.32%.
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Edgar has $7,000 in an account that earns 15% interest compounded annually. To the nearest cent, how much interest will he earn in 3 years?
Answer:
429
Step-by-step explanation:
Answer:
Edgar will earn $3,646.30 in interest over 3 years.
Step-by-step explanation:
I'd be happy to walk you through the problem step by step!
The problem is asking how much interest Edgar will earn in 3 years on an initial deposit of $7,000 that earns 15% interest compounded annually.
To solve this problem, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (the initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years) the money is invested
We are given that:
P = $7,000
r = 15% = 0.15 (as a decimal)
n = 1 (compounded annually)
t = 3 years
Now, we can plug these values into the formula and solve for A, which is the final amount including interest:
A = $7,000(1 + 0.15/1)^(1*3)
We simplify the expression inside the parentheses first, by dividing the annual interest rate by the number of times the interest is compounded per year:
A = $7,000(1.15)^(3)
We raise 1.15 to the power of 3 using a calculator or by multiplying 1.15 by itself 3 times:
A = $7,000(1.5209)
We multiply the initial deposit by the final amount including interest to get the total amount of interest earned:
Interest = $7,000(1.5209) - $7,000
We simplify the expression:
Interest = $10,646.30 - $7,000
Interest = $3,646.30
So, Edgar will earn $3,646.30 in interest over 3 years.
Hope this helped! If it didn't, I'm sorry! If you still need more help on this, ask me! :]
Solve for x. Round your final answer to the nearest tenth.
Law of cosines.
55 90 50
Answer: the length of side c is approximately 74.3 units.
Step-by-step explanation: In a triangle with sides a, b, and c, and opposite angles A, B, and C, respectively, the Law of Cosines states that:
c^2 = a^2 + b^2 - 2ab*cos(C)
We are given the following information:
a = 55 (the side opposite angle A)
b = 50 (the side opposite angle B)
C = 90 degrees (the angle opposite side c)
Substituting these values into the Law of Cosines, we get:
c^2 = 55^2 + 50^2 - 2(55)(50)*cos(90)
c^2 = 3025 + 2500 - 0
c^2 = 5525
Taking the square root of both sides, we get:
c = sqrt(5525)
c ≈ 74.3
List all the outcomes when rolling a fair six-sided die. a. What is the probability of getting a 1, 3, or a 6? (ALL ANSWERS SHOULD BE IN FRACTION FORM) b. What is the probability of getting a number less than 5? (ALL ANSWERS SHOULD BE IN FRACTION FORM)
Answer:
The outcomes when rolling a fair six-sided die are: 1, 2, 3, 4, 5, and 6.
a. The probability of getting a 1, 3, or a 6 is 3/6 or 1/2.
b. The probability of getting a number less than 5 is 4/6 or 2/3.
The angle of elevation from the spot where a basketball player is standing up to the
top of a 10ft high hoop is 25 degrees. How far is the player from the base of the hoop
(to the nearest hundredth of a foot)?
If the angle of elevation from the spot where a basketball player is standing up to the top of a 10ft high hoop is 25 degrees, the player is approximately 21.45 feet away from the base of the hoop.
To solve this problem, we can use the trigonometric function tangent, which relates the opposite side of a right triangle to its adjacent side, using the angle of elevation:
tan(25 degrees) = opposite / adjacent
where the opposite side is the height of the hoop (10 feet), and we need to find the adjacent side, which is the distance from the player to the base of the hoop.
To isolate the adjacent side, we can rearrange the equation:
adjacent = opposite / tan(25 degrees)
adjacent = 10 / tan(25 degrees)
Using a calculator, we can find that tan(25 degrees) is approximately 0.4663:
adjacent = 10 / 0.4663
adjacent ≈ 21.45 feet
We round to the nearest hundredth of a foot, which gives us the final answer of 21.45 feet.
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Bernie wanted to stock up on drinks for an upcoming party. first, he spent $37 on 7 cases of juice and 8 cases of soda, which is all the store had in stock. A few days later, he returned to the store and purchased an additional 7 cases of juice and 15 cases of soda, spending a total of $51. What is the price of each drink?
The price of each drink is given as follows:
Case of juice: $3.Case of soda: $2.How to obtain the price of each drink?The price of each drink is obtained by a system of equations, for which the variables are given as follows:
Variable x: cost of a case of juice.Variable y: cost of a case of soda.He spent $37 on 7 cases of juice and 8 cases of soda, hence:
7x + 8y = 37.
Purchased an additional 7 cases of juice and 15 cases of soda, spending a total of $51, hence:
7x + 15y = 51.
Hence the system is composed by these two equations:
7x + 8y = 37.7x + 15y = 51.Subtracting the second equation by the first, the value of y is obtained as follows:
7y = 14
y = 2.
Then the value of x is obtained as follows:
7x + 15(2) = 51
7x = 21
x = 21/7
x = 3.
More can be learned about a system of equations at https://brainly.com/question/30374328
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