Answer:
50.27
Step-by-step explanation:
Answer:
50.27
Step-by-step explanation:
A=1 /4 πd squared
A≈50.27
Hope this helps
If m + n = m, what is the value of n?
a. 1
b. 0
C.-1
d.not enough information to tell
Answer:
B. 0
Step-by-step explanation:
if n is anything but 0 then the answer wouldn't be m it would be for example m - 1 or m + 1
for it to remain m then n must be 0
a box used for shipping a volleyball set measures 10 inches by 20 inches by 40 inches. what is the longest length of support pole that will fit into the box, rounded to a tenth of an inch?
Answer:
45.8 inches
Step-by-step explanation:
Considering the given dimensions and taking 40 inches for length, 20 inches for height and 10 inches for width. The diagonal that runs from bottom to top of box will give the longest possible length of a pole.
Diagonal at the bottom of box
Diagonal=√(l²+w²)
Where l and w represent length and width respectively
Diagonal=√(40²+10²)=√1700
Diagonal between the height and bottom diagonal
Longest diagonal=√(20²+√1700)=√2100=45.8257569495584
Rounded off, the diagonal is approximately 45.8 inches
The longest length of a support pole that will fit into the box measures approximately 45.8 inches.
Explanation:To find the longest length of a support pole that will fit into the box, we need to determine the length of the diagonal of the box. The diagonal length can be found using the formula:
diagonal = √(length^2 + width^2 + height^2)
Substituting the given values:
diagonal = √(10^2 + 20^2 + 40^2) = √(100 + 400 + 1600) = √2100 ≈ 45.82 inches.
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Solve the inequality below; Which direction will the graph go in and will the dot be open or closed? m+5>-1
Answer:
The dot will be closed, and to the right from -6
Step-by-step explanation:
We can rearrange [tex]m+5>-1 = -6 < m[/tex]
As it is only a < we close the dots. It must go to the left as m is greater than -6 - all numbers greater than a value will be to the right on the number line.
An employee’s salary for Alar Services is $37,500. Next year, she will get an 8% increase in salary. How much is her new salary
Answer:
$40,500 I took a test and this was the answer to the question.
Answer:
$40500
Step-by-step explanation:
A car moves at 45 miles per hour. The time and the distance it travels are recorded.
What is the dependent variable?
the car
the time
the distance
45
Answer:
the distance
Step-by-step explanation:
More time care travels, more distance it goes. So distance depends of the time.
What is the approximate value of irrational number e (round to 5 decimal places)?
Answer:
2.71828
Step-by-step explanation:
In this question, we are asked to give the approximate value of the irrational number e.
We should understand that just like Pi, which is the ratio of the circumference of a circle to the diameter, we have the number called e. It is also a consistent like Pi and has an approximate value of 2.71828.
What does it mean when it is called irrational? it is an irrational number because it doesn’t have an exact fraction which is the ratio of two numbers and thus it has a non-ending list of numbers after the decimal point.
Final answer:
The irrational number e, also known as Euler's number, is approximately 2.71828 when rounded to five decimal places. It is crucial in mathematics, particularly calculus.
Explanation:
The question asks for the approximate value of the irrational number e rounded to five decimal places. The number e is a fundamental constant in mathematics, often referred to as Euler's number, which is approximately equal to 2.71828 when rounded to five decimal places.
This number plays a crucial role in various branches of mathematics, especially in calculus, relating to the rate of growth or decay in natural phenomena.
Mike discovered that the pool in his backyard is leaking slowly. The pool holds 18,968 gallons of water, and is leaking at a rate of 12 gallons per day. If mike does not replace the water that has leaked from the pool, how many gallons of water will remain in the pool after 68 days?
Answer:
18,152 Gallons
Step-by-step explanation:
First, you'll want to put this into an equation. We'll use x as the amount of water in gallons that will remain in the pool.
18,968 - 12 (68) = x
First, we'll multiply - 12 and 68.
We'd end up with this:
18,968 - 816 = x
From here, we can just subtract 816 from 18,968.
18,152 = x
Now we can see that there will be 18,152 gallons of water left in the pool after 68 days.
Santiago receives $143 per year in simple interest from three investments. Part is invested at 2%, part at 3%, and part at 4%. There is $500 more invested at 3% than at 2%. The amount invested at 4% is three times the amount invested at 3%. Find the amount of each rate
Please answer I need a lot of help on this!!!
Answer:
02a+.03b+.04c=126,
b=a+500,
c=3b
a=300., b=800., c=2400.
Step-by-step explanation:
The amount of each rate of interest given the total simple interest received is
$400, $900 and $2,700 respectively
let
a = 2% investment
= 0.02
b = 3% investment
= 0.03
c = 4% investment
= 0.04
Total interest = (0.02×a) + (0.03×b) + (0.04×c)
143 = 0.02a + 0.03b + 0.04c (1)
b = a + 500 (2)
c = 3b (3)
substitute (3) into (1)
143 = 0.02a + 0.03b + 0.04(3b)
143 = 0.02a + 0.03b + 0.12b
0.02a + 0.15b = 143 (4)
from (2)
b - a = 500 (5)
multiply (5) by 0.02
0.02b - 0.02a = 10
0.02a + 0.15b = 143 (4)
Add
0.02b + 0.15b = 10 + 143
0.17b = 153
b = 900
substitute b into (3)
c = 3b (3)
c = 3(900)
c = 2700
Recall,
b = a + 500 (2)
900 = a + 500
900 - 500 = a
a = 400
Therefore, the amount of each rate of interest given the total simple interest received is $400, $900 and $2,700 respectively
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A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 38,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 37,300 miles with a standard deviation of 1000 miles. At α= 0.05, does the test suggest that mean life is less than 39000 miles?
Answer:
[tex]t=\frac{37300-38000}{\frac{1000}{\sqrt{18}}}=-2.970[/tex]
[tex]p_v =P(t_{17}<-2.97)=0.0043[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower than 38000 at 5% of signficance.
Step-by-step explanation:
We assume this question: A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 38,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 37,300 miles with a standard deviation of 1000 miles. At α= 0.05, does the test suggest that mean life is less than 38000 miles? because if is not this one is not appropiate
Data given and notation
[tex]\bar X=37300[/tex] represent the sample mean
[tex]s=100[/tex] represent the sample standard deviation for the sample
[tex]n=18[/tex] sample size
[tex]\mu_o =7500[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is lower than 38000, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 38000[/tex]
Alternative hypothesis:[tex]\mu < 38000[/tex]
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{37300-38000}{\frac{1000}{\sqrt{18}}}=-2.970[/tex]
P-value
The degrees of freedom are given by:
[tex] df = n-1= 18-1=17[/tex]
Since is a left tailed test the p value would be:
[tex]p_v =P(t_{17}<-2.97)=0.0043[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower than 38000 at 5% of signficance.
The shipping firm's hypothesis test determines that the mean lifespan of a particular brand of tires is indeed less than 38,000 miles based on their sample data and the significance level.
Explanation:The shipping firm is performing a hypothesis test about a population mean, where the suspected value is 38,000 miles. The null hypothesis (H0) would be that the mean life of the tires is equal to 38,000 miles, while the alternative hypothesis (H1) is that the mean life is less than 38,000 miles.
Using the provided sample data, we can calculate the test statistic (z-score), which helps us determine the p-value. The test statistic is given by (Sample Mean - Pop Mean) / (Standard Deviation / sqrt(n)) = (37300 - 38000) / (1000 / sqrt(18)). This gives us a test statistic of -3.1623.
We also know that our α is 0.05 for this problem. Now we find the p-value that is associated with this test statistic. If the p-value is less than our alpha, we reject the null hypothesis. Given our test statistic, we will indeed find a very low p-value, less than 0.05, which means we reject the null hypothesis and conclude the mean lifespan of the tires is less than 38,000 miles.
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Find the surface area of the cube shown below 2 1/2
Answer:
37.5
Step-by-step explanation:
Answer:
37.5
Step-by-step explanation:
f(x) goes through the point (9,2) then the function f(3x) must go through what point
Answer:
(27,2)
Step-by-step explanation:
Multiply the x value by 3 to get the transformation
If a function f(x) goes through the point (9,2), the function f(3x) will go through the point (3,2) after substituting x with 3x in the original function.
If the function f(x) passes through the point (9,2), then to determine the corresponding point that f(3x) goes through, we must substitute x with 3x in the original function.
Since we know that f(9) = 2, to find f(3x) we look for a value of x that when multiplied by 3 gives us 9.
That value is x = 3.
Therefore, f(3×3) = f(9) = 2, meaning f(3x) will go through the point (3,2).
Alice, Betty and Carol all have the same amount of money (more than 50 cents but less than a dollar). Alice has two coins, Betty and Carol each have 3 coins, but Betty and Carol do not have any coins that are the same. How much money does each girl have?
Answer:
Each girl has 60 cents.
Step-by-step explanation:
Since they have between 50 cents and 1 dollar, then Alice should have a 50 cent coin and 1 coin of less value (because if she had 2 coins that are worth 25 cents or less, she would have only 50 cents at most).
On the other hand, Both betty and carol need to have a coin that is at least 25 cents worth (because otherwise they would have 30 cents at most), but since they cant have the same coins, then one of them should have one 50 cent coin (and 2 small cent coins) and the other should have at least two twenty five cent coins.
Lets assume that Betty has a 50 cent coin and Carol has two 25 cent coins. Since Alice also has a 50 cent coin, then the remaining coin of Alice should have the same value than the sum of the remaining 2 coins that Betty has.
The values of the coins are 5,10, 25, 50, and 100. Since they cant have 1 dollar coins, then the only possibility for a coin to have the sum of the values of 2 coins is to have a value of 10 (10 = 5+5). Thus:
Alice has one coin of 50 cents and one coin of 10 centsBetty has one coin of 50 cents and two coins of 5 centsCarol has two coins of 25 cents and one coin of 10 centsEach girl has 50+10 = 50+5+5=25+25+10 = 60 cents
Hey, please answer the attachment questions. 3 questions.
Answer:
A. Cat
B. 8
C. 6 people
Step-by-step explanation:
A. Just by looking at it Cat has the least amount of squares
B. There are 10 full squares in total (including the pieces). 80 people divided by 10 boxes is 8.
C. There is 1/2 and 1/4 more people who picked giraffe more than dogs. 1
1/2 of 8 is 4. 1/4 of 8 is 2. 4+2 = 6.
Using the table tool, create a truth table for the compound statement ~(p^q)
Answer:
The image attach is the truth table for the compound statement
Step-by-step explanation:
Write the number 0.00008623 in standard form
Answer:
8.623
Step-by-step explanation:
ik it
Answer: 8.623
Step-by-step explanation: you move the decimal down 6 points left and then you get your answer
Olivia is cutting a 1 \dfrac12 \text{ m}1 2 1 m1, start fraction, 1, divided by, 2, end fraction, start text, space, m, end text by \dfrac34\text{ m} 4 3 mstart fraction, 3, divided by, 4, end fraction, start text, space, m, end text piece of rectangular paper into two pieces along its diagonal. Find the area of each of the pieces.
Answer: 9/6 metre
Step-by-step explanation:
From the question, Olivia is cutting a 1 1/2m by 3/4m piece of rectangular paper into two pieces along its diagonal
This will result into two congruent triangular pieces.
Let us first find the area of each piece by finding the area of the original rectangle and dividing it by two.
The area of a rectangle is given by multiplying the length and the width:
1 1/2 × 3/4
We can change the first fraction to an improper fraction:
(1×2)+1 = 2+1 = 3; this gives us 3/2:
3/2 × 3/4 = 9/8 = 1 1/8
The area of the entire rectangle is 1 1/8 sq. m., or 1.125 sq. m.
Divide this by 2:
9/8 ÷ 2
9/8 × 1/2 = 9/16
The area of each rectangle is 9/16 sq. m., or 0.5625 sq.
Answer:
9/16
Step-by-step explanation:
Write a quadratic function whose graph has a vertex of (3, 2) and passes through the point (4, 7), using f(x) = a(x - h)^2 + k (vertex form).
THANK YOU FOR HELPING!!!
The quadratic function is f(x) = 5(x - 3)² + 2.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
where (h, k) is the vertex of the parabola.
We are given that the vertex is (3, 2), so we have:
h = 3
k = 2
We also know that the parabola passes through the point (4, 7).
We can use this point to find the value of a:
7 = a(4 - 3)² + 2
5 = a
Therefore, the quadratic function is:
f(x) = 5(x - 3)² + 2
This quadratic function has a vertex of (3, 2) and passes through the point (4, 7).
Thus,
The quadratic function is f(x) = 5(x - 3)² + 2.
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A county is considering rasing the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour. a random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour. at alpha equals 0.10, do you have enough evidence to support the county's claim? complete parts (a) through (d) below.
Answer:
No, at alpha equals 0.10, we do not have enough evidence to support the county's claim.
Step-by-step explanation:
We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.
A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.
Let [tex]\mu[/tex] = true mean speed of the vehicles.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30 miles per hour {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 miles per hour {means that the mean speed of vehicles is greater than 30 miles per hour}
The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean speed of 15 vehicles = 31 mph
s = sample standard deviation = 4.7 mph
n = sample of vehicles = 15
So, test statistics = [tex]\frac{31-30}{\frac{4.7}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= 0.824
Hence, the value of test statistics is 0.824.
Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.
What are the answers
Answer:
x = 1, y = 1
Step-by-step explanation:
Use system of equations to solve for x and y by using substitution
The solution to the system of equations, though we can solve using substitution, can also be found by graphing these equations. If you graph these equations, look for where they intersect (it should be one point!).
-5x + 6 = 3x - 2
6 = 8x - 2
8x = 8
x = 1
y = 3(1) - 2
y = 3 - 2
y = 1
Hope this helps!! :)
3. Solve each division problem (reduce if possible):
1/5 divided by 1/10
Answer:
2
Step-by-step explanation:
Because to divde to fractions you multiply the first fraction by the second’s reciprocal. The reciprocal is when you switch the numerator and the denominator.In this case 1/5 times 10/1 which is 2.
Explain why a cross section of a polyhedron does not always match the base of that polyhedron.
Explanation:
A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.
If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.
For example, the cross sections of a cube include ...
triangle, square, rectangle, trapezoid, general quadrilateral, pentagon, hexagon
Answer: A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.
If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.
Step-by-step explanation.
can some one pls Use elimination to solve each system of equations
2x - y = -1
3x - 2y = 1
Answer:
Correct answer: x = - 3 and y = - 5
Step-by-step explanation:
Given:
2 x - y = - 1
3 x - 2 y = 1
We will multiply first equation with number (- 2) and get:
- 4 x + 2 y = 2
then we add this equation to another and get:
- 4 x + 3 x = 2 + 1
- x = 3 / · (- 1)
x = - 3
now we replace x = - 3 in the first equation and get:
2 (- 3) - y = - 1 ⇒ - 6 - y = - 1 / ·(- 1) ⇒ 6 + y = 1 y = 1 - 6 = - 5
y =- 5
God is with you!!!
Answer:
x= -3
y= -5
Step-by-step explanation:
-2 (2x-y= -1) = -4x + 2y = 2
-4x + 2y = 2
3x - 2y = 1
-------------------
-x = 3
x = -3
plug the x= -3 into the equation to find y
Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a 0 bit and a 1 bit are equally likelyb) the probability that a bit is a 1 is 0.6c) the probability that the i-th bit is a 1 is 1/(2^i) for i=1,2,3,...,10
Answer:
A) 0.0009765625
B) 0.0060466176
C) 2.7756 x 10^(-17)
Step-by-step explanation:
A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10
If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5
Now the definition of binomial probability is given by;
P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)
Now, we want the definition of this probability at k = 10.
Thus;
P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)
P(x = 10) = 0.0009765625
B) here we are given that p = 0.6 while n remains 10 and k = 10
Thus;
P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)
P(x=10) = 0.0060466176
C) we are given that;
P((x_i) = 1) = 1/(2^(i))
Where i = 1,2,3.....,n
Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;
P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)
This gives;
P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]
This gives;
P(x = 10) = [1/(2^(55))]
P(x = 10) = 2.7756 x 10^(-17)
Final answer:
To find the probability that a randomly generated bit string of length 10 does not contain a 0, we consider each scenario separately. For equally likely 0s and 1s, the probability is (0.5)^10. For a 0.6 probability of 1, the probability is (0.4)^10. For varying probabilities of 1, the probability is calculated by multiplying the probabilities for each position.
Explanation:
To find the probability that a randomly generated bit string of length 10 does not contain a 0, we need to consider each scenario separately.
a) If a 0 bit and a 1 bit are equally likely, then the probability of getting a 0 in any position is 0.5. Since the bits are independent, the probability of not getting a 0 in any of the 10 positions is (0.5)^10 = 0.00097656.
b) If the probability of a bit being a 1 is 0.6, then the probability of getting a 0 in any position is 1 - 0.6 = 0.4. Again, since the bits are independent, the probability of not getting a 0 in any of the 10 positions is (0.4)^10 = 0.00604661.
c) If the i-th bit has a probability of 1/(2^i) of being a 1, then the probability of getting a 0 in the i-th position is 1 - 1/(2^i). Multiplying the probabilities for each position gives us the probability of not getting a 0 in any of the 10 positions.
P(Not getting a 0) = (1 - 1/(2^1))(1 - 1/(2^2))(1 - 1/(2^3))(1 - 1/(2^4))(1 - 1/(2^5))(1 - 1/(2^6))(1 - 1/(2^7))(1 - 1/(2^8))(1 - 1/(2^9))(1 - 1/(2^10)) = 0.00563108.
Is this statement true or false 16% of 250 is equal to 250% of 16
16% of 250 is .16 * 250, which is 40
250% of 16 is 2.5 * 15, which is also 40
So, it's true.
A percentage is a way to describe a part of a whole. The statement that 16% of 250 is equal to 250% of 16 is true.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The value of 16% of 250 can be written as,
[tex]16\%\ of\ 250\\\\=\dfrac{16}{100} \times 250\\\\=40[/tex]
The value of 250% of 16 can be written as,
[tex]250\%\ of\ 16\\\\=\dfrac{250}{100} \times 16\\\\=40[/tex]
Thus, the statement that 16% of 250 is equal to 250% of 16 is true.
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Which is a y-intercept of the continuous function in the table? (5, 0) (0, 1) (0, 5) (1, 0)
The possible y-intercepts for the given continuous function from the table are (0,1) and (0,5).
Explanation:In this mathematical problem, the student is asking about the y-intercept of a function represented in a table. The y-intercept of a continuous function is a point where the line of the function intersects or touches the y-axis on a graph. This point is always (0, y). If we look at the given points, only (0,1) and (0,5) can potentially be y-intercepts because they have 0 as their x-coordinate, which is the requirement for a point to be a y-intercept.
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At a baseball game, 95% of people attending were supporting the home team, while 5% were supporting the visiting team. If the total number of people attending the game was 1000, how many people attending were supporters of the home team?
Answer:
950 people
Step-by-step explanation:
95% of people attending supported the home team.
1000 people attended the game.
That means that 95% of 1000 people supported the home team.
We need to find 95% of 1000.
To find a percent of a number, multiply the percent by the number. First, change the percent into a decimal by by moving the decimal point two places to the left. Then multiply the percent written as a decimal by the number.
95% of 1000 =
= 95% * 1000
= 0.95 * 1000
= 950
Answer: 950 people
A license plate is to consist of 5 digits followed by 5 uppercase letters. Determine the number of different license plates possible if the first and second digits must be odd, and repetition is not permitted.
Answer:
[tex]5.3044992\times 10^{10}[/tex]
Step-by-step explanation:
We are given that a license plate consist of 5 digits and 5 uppercase letters
Digits used=0,1,2,..9
Total number of letters=26
Repetition is not allowed
Total number of odd digits=(1,3,5,7,9)=5
The first place filled by 5
Second place filled by 4
Third place filled by 8
Fourth place filled by 7
Fifth place filled by 6
Sixth place filled by 26
Seventh place filled by 25
Eighth place filled by 24
Ninth place filled by 23
Tenth place filled by 22
Total number of possible different license plates =[tex]5\times 4\times 8\times 7\times 6\times 26\times 25\times 24\times 23\times 22[/tex]=[tex]5.3044992\times 10^{10}[/tex]
The number of possible license plates, considering the restrictions on the first and second odd digits and no repetition, is 53,144,832,000. This was determined by systematically calculating the choices for each digit and letter and then multiplying them together.
Calculating the Number of Different License Plates
To determine the number of different license plates possible, we need to consider two sections: the digits and the letters. The first and second digits must be odd, and repetition of digits and letters is not permitted.
Step-by-Step Calculation:
→ First digit: Since it must be odd (1, 3, 5, 7, 9), there are 5 choices.
→ Second digit: Also must be odd but different from the first, so there are 4 remaining choices.
→ Third digit: Any digit except the first two, leaving 8 choices.
→ Fourth digit: Any remaining digit, leaving 7 choices.
→ Fifth digit: Any remaining digit, leaving 6 choices.
→ First letter: Any uppercase letter, 26 choices.
→ Second letter: Any remaining uppercase letter, 25 choices.
→ Third letter: Any remaining uppercase letter, 24 choices.
→ Fourth letter: Any remaining uppercase letter, 23 choices.
→ Fifth letter: Any remaining uppercase letter, 22 choices.
→ Multiply these choices together:
5 × 4 × 8 × 7 × 6 × 26 × 25 × 24 × 23 × 22
→ Calculate the total:
5 × 4 × 8 × 7 × 6 = 6720
26 × 25 × 24 × 23 × 22 = 7893600
6720 × 7893600 = 53,144,832,000
Therefore, the number of different license plates possible is 53,144,832,000.
Verify the identity. StartFraction sine (alpha plus beta )Over cosine alpha cosine beta EndFraction equals tangent alpha plus tangent beta Rewrite the numerator on the left side of the identity using one of the sum and difference formulas. StartFraction nothing Over cosine alpha cosine beta EndFraction Rewrite the fraction from the previous step such that it is a sum or difference of two expressions. Do not simplify the result. nothing Divide out any common factors in the expression from the previous step. nothing The expression from the previous step then simplifies to tangent alpha plus tangent beta using what? A. Quotient Identity B. Reciprocal Identity C. Even-Odd Identity D. Pythagorean Identity
Answer:
(A)Quotient Identity
Step-by-step explanation:
To Prove: [tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\tan \left(\alpha +\beta \right)[/tex]
Rewrite the numerator on the left side of the identity using the sum and difference formulas.
[tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\dfrac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta -\sin \alpha \sin \beta }[/tex]
Next, Divide the numerator and denominator by[tex]cos\alpha \text{cos}\beta[/tex]
[tex]=\dfrac{\frac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta }}{\frac{\cos \alpha \cos \beta -\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Rewrite the fraction from the previous step such that it is a sum or difference of two expressions as shown below
[tex]=\dfrac{\frac{\sin \alpha{\cos \beta }}{\cos \alpha{\cos \beta }}+\frac{{\cos \alpha }\sin \beta }{{\cos \alpha }\cos \beta }}{\frac{{\cos \alpha }{\cos \beta }}{{\cos \alpha }{\cos \beta }}-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Divide out any common factors in the expression from the previous step.
[tex]=\dfrac{\frac{\sin \alpha }{\cos \alpha }+\frac{\sin \beta }{\cos \beta }}{1-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
The expression from the previous step then simplifies to [tex]\tan \left(\alpha +\beta \right)[/tex] using the Quotient Identity
[tex]=\dfrac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\tan \left(\alpha +\beta \right)[/tex]
In the right triangle shown, measure of angle A equals 45 degrees and the measure of AB equals 12. How long is BC?
Answer:
think ab = 4
Step-by-step explanation:
What is the value of this expression when x = negative 1 and y = 2?
4 x cubed y squared
Answer:
the correct answer is -16
Step-by-step explanation:
I took the test
The solution for the expression 4x³y² at x = -1 and y =2 will be -16.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the expression is 4x³y². The values of x and y are -1 and 2.
The expression at the values of x and y will be solved as:-
E = 4x³y²
Substitute the values of x = -1 and y = 2.
E = 4x³y²
E = 4 x ( -1)³ x ( 2 )²
E = 4 x -1 x 4
E = -16
The value of the expression at x =-2 and y = 2 will be -16.
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