The given set of vectors which are represented as {(1, -4), (4, 1)} is orthogonal.
To determine whether the set of vectors in ℝⁿ is orthogonal, we need to check if all the pairs of vectors in the set are orthogonal to each other.
In this case, the set of vectors is {(1, -4), (4, 1)}. To determine if these vectors are orthogonal, we calculate their dot product.
The dot product of two vectors (a, b) and (c, d) is given by a * c + b * d.
For the first pair of vectors (1, -4) and (4, 1), the dot product is 1 * 4 + (-4) * 1 = 4 + (-4) = 0.
Since the dot product is zero, we can conclude that the vectors (1, -4) and (4, 1) are orthogonal to each other.
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I dont know the answer please help me yall
Answer:
180 customers made additional purchases
Step-by-step explanation:
In order to find the percent of something like 72% of 250 you need to convert the percentage to a decimal and multiply it to the number.
0.72 * 250 = 180
Answer:
180 customers
Step-by-step explanation:
Since 72% of the customers made additional purchases and there were 250 customers, we need to look for 72% of 250. To do this we convert 72 into a fraction, which makes it 0.72 and we turn the word "of" into a multiplication symbol (as of most commonly means multiplication in math). So, 0.72*250=180. Therefore, 180 customers made additional purchaces.
Question: Find the M
Answer:
<ABC = 17
Step-by-step explanation:
I'm going to make a guess. My guess is that you want the measure of angle B. I didn't see that the diagram asks that very question.
If you join <ADC, that angle is also 34 degrees. By the property of angles touching the circumference of a circle, the angle touching the circumference is 1/2 the central angle
1/2 34 = 17
what angle is opposite the longest side?
I will mark as brainliest
Answer:
75
Step-by-step explanation:
Answer:
the angle that is 75 degrees
Step-by-step explanation:
Because the longest side is always opposite of the largest angle and the smallest side is always opposite of the smallest angle.
Will the following variables have positive correlation, negative correlation,
or no correlation? Number of managers on staff at a restaurant and number
of waiters on staff
Answer:
Step-by-step explanation:
What is the approximate surface area of this right prism with triangular bases?
Answer:
394.2 ft
Step-by-step explanation:
7.8(9)=70.2
This is the measurement for the two triangular sides
9(12)(3)=324 This is the measurement for the three triangular sides
70.2 +324 = 394.2 APPROX
The expression shown below was generated using a graphing calculator. Solve the expression and answer in correct scientific notation.
(4.5E6)(2.3E7)
A) 1.035×1014
B) 1.035×1013
C) 6.8×1013
D) 2.2×1013
Graph y=\dfrac{2}{7}\,xy= 7 2 xy, equals, start fraction, 2, divided by, 7, end fraction, x.
Answer:
The answer is A, C, and D
The graph should be 7 units for x and 2 units for y.
Step-by-step explanation:
Full Question: Graph y = 2/7x
Look at attachment:
Hope this helps! :)
The graph of the linear function y = (2/7)x will be given below.
What is the graph of the function?The collection of all coordinates in the planar of the format [x, f(x)] that make up a variable function's graph.
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The function is given below.
y = (2/7)x
Compare the function with standard equation of the line,
Then the slope of the function is 2/7 and the y-intercept is zero, that means the line is passing through origin.
Then the graph of the linear function y = (2/7)x will be given below.
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Determine which set of side measurements could be used to form a right triangle.
12, 16, 20
6, 14, 19
6, 8, 15
4, 5, 6
Only the side lengths 12, 16, and 20 can be used to create a right triangle.(Option-A)
The Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides, must be satisfied for a set of side measurements to create a right triangle.
This theorem allows us to determine which sets of side measurements can create a right triangle. 202 = 400 for the set of measures 12, 16, and 20.
[tex]12^2 + 16^2[/tex] = 144 + 256 = 400
The measurements could result in a right triangle because they meet the Pythagorean theorem.
Measurements 6, 14, and 19 are as follows: 192 = 361 62 + 142 = 36 + 196 = 232 . (Option-A)
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Answer:
12, 16, 20
Step-by-step explanation:
A right triangle is a triangle that has one right angle, which is an angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse. The other two sides are called the legs.
We can use the Pythagorean theorem to determine which set of side measurements. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
So, for each set of side measurements, we can calculate the square of each side and add them together. If the sum is equal to the square of the hypotenuse, then the set of side measurements could be used to form a right triangle.
Set 1: 12, 16, 20
Square of 12: 144Square of 16: 256Square of 20: 400The sum of the squares of the legs is 144 + 256 = 400.
The square of the hypotenuse is also 400.
Therefore, set 1 could be used to form a right triangle.
Set 2: 6, 14, 19
Square of 6: 36Square of 14: 196Square of 19: 361The sum of the squares of the legs is 36 + 196 = 232.
The square of the hypotenuse is 361.
Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 2 could not be used to form a right triangle.
Set 3: 6, 8, 15
Square of 6: 36Square of 8: 64Square of 15: 225The sum of the squares of the legs is 36 + 64 = 100.
The square of the hypotenuse is 225.
Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 3 could not be used to form a right triangle.
Set 4: 4, 5, 6
Square of 4: 16 Square of 5: 25 Square of 6: 36The sum of the squares of the legs is 16 + 25 = 41.
The square of the hypotenuse is 36.
Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 4 could not be used to form a right triangle.
Therefore, the only set of side measurements that could be used to form a right triangle is set 1.
4) Of all the registered automobiles in Colorado, 10% fail the state emissions test. Ten automobiles are selected at random to undergo an emissions test. a. Find the probability: (Provide your answer with three decimal places) 1) That exactly three of them fail the test. [2 pts] 11) That fewer than three of them fail the test. [3 pts] 1) That at least eight of them fail the test. [3 pts] b. Find the mean, variance, and standard deviation of the number of automobiles fail the test. (Round your answers to three decimal places if needed) (5 pts]
The mean is 1, variance is 0.9, and standard deviation is 0.948, rounded to three decimal places. Given data: Of all the registered automobiles in Colorado, 10% fail the state emissions test.
Ten automobiles are selected at random to undergo an emissions test.a. Find the probability:
1) That exactly three of them fail the test.
For the number of success (x) and number of trials (n),
the probability mass function (PMF) for binomial distribution is given by: [tex]P(X = x) = C(n, x) * p^{(x)} * q^{(n-x)},[/tex]
where [tex]C(n, x) = (n!)/((n-x)! * x!) ,[/tex]
p and q are the probabilities of success and failure, respectively. Here, the probability of success is the probability of an automobile to fail the test, p = 0.10 and the probability of failure is q = 1 - p = 0.90.
Now, X is the number of automobiles that fail the test.
Thus, n = 10, x = 3, p = 0.10, and q = 0.90.
Using the above formula:
[tex]P(X = 3) = C(10, 3) * (0.10)^{(3)} * (0.90)^{(10-3)}\\= 0.057[/tex]
The required probability is 0.057, rounded to three decimal places.
1) That fewer than three of them fail the test.
The required probability is P(X < 3).P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) Using the above formula:
[tex]P(X = 0) = C(10, 0) * (0.10)^{(0)} * (0.90)^{(10)}[/tex]
= 0.3487P(X = 1)
= [tex]C(10, 1) * (0.10)^{(1) }* (0.90)^{(9)}[/tex]
= 0.3874P(X = 2) = [tex]C(10, 2) * (0.10)^{(2)} * (0.90)^{(8)}[/tex]
= 0.1937
Now, P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.3487 + 0.3874 + 0.1937
= 0.9298
The required probability is 0.9298, rounded to three decimal places.
1) That at least eight of them fail the test.
The required probability is
P(X ≥ 8).P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) Using the above formula:
[tex]P (X = 8) = C(10, 8) * (0.10)^{(8)} * (0.90)^{(2) }[/tex]
= 0.0000049
[tex]P(X = 9) = C(10, 9) * (0.10)^{(9)} * (0.90)^{(1) }[/tex]
= 0.0000001
[tex]P(X = 10) = C(10, 10) * (0.10)^{(10)} * (0.90)^{(0)}[/tex]
= 0.0000000001
Now,
P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)
= 0.0000049 + 0.0000001 + 0.0000000001 = 0.000005
The required probability is 0.000005,
rounded to three decimal places.
b. Find the mean, variance, and standard deviation of the number of automobiles fail the test.
The mean (μ) for binomial distribution is given by: μ = n * p,
where n is the number of trials and p is the probability of success.
The variance ([tex]= 1 \sigma ^ 2 = n * p * q = 10 * 0.10 * 0.90 ^2[/tex]) for binomial distribution is given by: [tex]\sigma ^2 = n * p * q[/tex]
The standard deviation (σ) for binomial distribution is given by:
σ = √(n * p * q)
Here, n = 10 and p = 0.10.
Thus, q = 0.90.
Using the above formulas:
μ = n * p = 10 * 0.10
[tex]= 1\sigma ^2 = n * p * q = 10 * 0.10 * 0.90[/tex]
= 0.9σ = √(n * p * q)
= √(10 * 0.10 * 0.90)
= 0.948
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A coastline recedes at a rate of 3cm per year. How much of the coastline dissappears after 4 years?
Answer:
12 cm of coastline
Step-by-step explanation:
Multiply the years (factor) by the receding amount, 3cm, (constant) BAM answer.
PLEASE HELP! What does x equal?
Step-by-step explanation:
(FE+BC)/2=<FDE
<FDE=<BDC
it is basically the average of x and 70.
(x+70)/2=104
x=138
Hope that helps :)
Answer:
The answer is probly 70 degrees
i might be wrong
i just hope this works
good luck
CAN SOMEONE PLEASE HELP ME PLEASE
Answer:
If Then proof has been explained below!
Step-by-step explanation:
1.) If segment XY ║ ZW, then the 154° angle ≅ ∠2 (vertical angles)
2.) If segment XY ║ ZW, then ∠2 is complementary to ∠4
3.) If ∠2 is complementary to ∠4, then ∠4 = 28°
I hope this helps! If you have any questions, feel free to add it into the comments and please rate my answer and consider marking as brainliest!
help pls plssssss now
Answer:
i would say B but i dont know
Step-by-step explanation:
bob is pulling a 30 kgkg filing cabinet with a force of 200 nn , but the filing cabinet refuses to move. the coefficient of static friction between the filing cabinet and the floor is 0.80.
Bob is exerting a force of 200 N on a 30 kg filing cabinet, but it remains stationary due to the static friction between the cabinet and the floor. The coefficient of static friction is given as 0.80.
The static frictional force acts between two surfaces in contact when there is no relative motion between them. The magnitude of static friction can be determined using the equation F_static = μ_static * N, where μ_static is the coefficient of static friction and N is the normal force.
In this scenario, Bob is applying a force of 200 N to the filing cabinet. In order to overcome the static friction and set the cabinet in motion, the applied force must be greater than or equal to the maximum static frictional force. The maximum static frictional force can be calculated by multiplying the coefficient of static friction with the normal force.
Since the cabinet is stationary, the applied force of 200 N is not sufficient to overcome the maximum static frictional force. The maximum static frictional force can be determined as F_static = μ_static * N = 0.80 * (30 kg * 9.8 m/s^2) = 235.2 N.
As the applied force of 200 N is less than the maximum static frictional force of 235.2 N, the filing cabinet remains stationary. Bob would need to apply a force greater than 235.2 N to overcome the static friction and set the cabinet in motion.
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Let f: X+R be a linear function, where X is a topological vector space. (a) Suppose that f is bounded above on a neighborhood V of the origin. That means there exists 7>0 such that f(x) < y for all x EV. Prove that there exists a neighborhood W of the origin such that f(x)
Given a linear function f: X -> R that is bounded above on a neighborhood V of the origin, we need to prove that there exists a neighborhood W of the origin such that f(x) < y for all x in W.
To prove this statement, we can use the properties of linear functions and the topology of X. Since f is linear, we know that f(0) = 0.
Let's consider the open ball B(0, y) centered at the origin with radius y. Since f is bounded above on V, there exists a constant M > 0 such that f(x) < M for all x in V.
Now, let's define a neighborhood W = V ∩ f^(-1)(B(0, y/M)). W is the intersection of V and the inverse image of the open ball B(0, y/M) under the function f.
By the properties of inverse images, we know that f(x) < y/M for all x in W.
Therefore, we have found a neighborhood W of the origin such that f(x) < y for all x in W, satisfying the condition we needed to prove.
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n the problem of estimating total hospitalization costs for kidney stone patients, suppose Muscat and Dhofar regions were selected as strata because they have very different incident rates for the disease, and the estimates for each region was needed separately. Also, this stratification into geographic regions simplified the sampling procedures. The sample data are summarized as follows: Muscat Dhofar ni=260 12=150 Mean cost ý,=170 RO Mean cost y =125 RO S =3050 $ -2525 G = 745 C-10 RO n 02-680 C2=12 RO A previous study showed the number of kidney stone incidents in the Muscat to be 325 out of 100,000 population and the number in the Dhofar to be 320 out of 100,000. The population of the Muscat was 775,878, and the population of the Dhofar was 249,729, according to the 2010 census. a) Obtain the estimates of N, and N2, the numbers of kidney stone patients expected to be found in the Muscat and Dhofar regions. b) Obtain the average annual cost of hospitalization of the kidney patients of the two region combined with 95% confidence interval and interpret the results. c) Find the appropriate sample size n and stratum sample size ni and n2 for estimating the population mean with a bound on the error of estimation equal to 50 RO, considering proportional allocation.
The estimated number of kidney stone patients in the Muscat region (N₂) is approximately 447,184, and in the Dhofar region (N₁) is approximately 128,694.
Given,
Estimation of total hospitalization costs for kidney stone patients .
Here,
To obtain the estimates of N and N, the numbers of kidney stone patients expected to be found in the Muscat and Dhofar regions, we can use the stratified sampling formula:
Nᵢ = (nᵢ / n) * N,
where:
- Nᵢ is the estimate of the population size in stratum i.
- nᵢ is the sample size in stratum i.
- n is the total sample size (sum of all stratum sample sizes).
- N is the total population size.
Given the information provided, we have the following data:
For Dhofar region:
- n₁ = 260 (sample size)
- N = 249,729 (population size according to the 2010 census)
For Muscat region:
- n₂ = 150 (sample size)
- N = 775,878 (population size according to the 2010 census)
Using the given formula, we can calculate the estimates for each region:
For Dhofar region:
N₁ = (n₁ / n) * N = (260 / (260 + 150)) * 249,729
For Muscat region:
N₂ = (n₂ / n) * N = (150 / (260 + 150)) * 775,878
To obtain the values, let's calculate them:
For Dhofar region:
N₁ = (260 / (260 + 150)) * 249,729 ≈ 128,694
For Muscat region:
N₂ = (150 / (260 + 150)) * 775,878 ≈ 447,184
Therefore, the estimated number of kidney stone patients in the Muscat region (N₂) is approximately 447,184, and in the Dhofar region (N₁) is approximately 128,694.
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The rectangular prism has a volume of 936 cubic inches. Write and solve an equation to find the missing dimension of the prism.
Answer: Solution in photo
divide 150 toys amongst two groups of children in the ratio 6:9
Answer:
60 and 90
Step-by-step explanation:
150/15 = 10
6 x 10 = 60
9 x 10 = 90
The required number of toys that can be divided among two groups is 60 and 90.
Given that,
To divide 150 toys amongst two groups of children in a ratio of 6:9.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Ratio = 6 / 9
Total of ratio = 15
Now,
For 1 group toys = 150 [6 / 15] = 60
For group 2 toys = 150 [9 / 15] = 90
Thus, the required number of toys that can be divided among two groups is 60 and 90.
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Compute the first 4 non-zero terms (if any) of the two solutions
linearly independent power series form centered on
zero for the Hermite equation of degree 2, that is y''-2xy'+4y=0
The power series solutions for the Hermite equation of 2 are zero for the first four terms of the given equation.
Equation = y''-2xy'+4y=0
The solutions can be expressed as power series using the Hermite equation of degree 2 can be calculated as:
y = ∑(n=0 to ∞) [tex]a_n x^{n}[/tex]
where [tex]a_n[/tex] is the coefficient of the nth term and x is the variable.
Differentiating y with regard to x,
y = ∑(n=0 to ∞) [tex]a_n x^{n-1}[/tex]
Double integrating the y with respect to x:
y'' = ∑(n=0 to ∞) [tex]a_nn(n-1)x^{n-2}[/tex]
Substituting the above equation in the Hermite equation
∑(n=0 to ∞) [tex]a_nn(n-1)x^{n-2}[/tex] - 2x∑(n=0 to ∞) [tex]a_n x^{n-1}[/tex] + 4∑(n=0 to ∞) [tex]a_n x^{n}[/tex] = 0
∑(n=0 to ∞)[tex][a_n(n(n-1) - 2n + 4)] x^{n}[/tex] = 0
Taking the coefficients of each term as zero:
[tex]a_n[/tex](n(n-1) - 2n + 4) = 0
The first four non-zero terms:
If n = 0,
[tex]a_o[/tex](0(0-1) - 2(0) + 4) = 0
[tex]a_o[/tex](4) = 0
[tex]a_o[/tex] = 0
If n = 1,
[tex]a_1[/tex](1(1-1) - 2(1) + 4) = 0
[tex]a_1[/tex](2) = 0
[tex]a_1[/tex] = 0
If n= 2,
[tex]a_2[/tex](2(2-1) - 2(2) + 4) = 0
[tex]a_2[/tex](2) = 0
[tex]a_2[/tex]= 0
If n = 3,
[tex]a_3[/tex] (3(3-1) - 2(3) + 4) = 0
[tex]a_3[/tex] (2) = 0
[tex]a_3[/tex] = 0
Therefore we can conclude that the power series solutions for the Hermite equation of 2 are zero.
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Pennies made prior to 1982 were made of 95% copper Because of their copper content, these pennies are worth about $0.023 each. Pennies made after 1982 are only 2.5% copper Jenna reads online that 13.2% of pennies in circulation are pre-1982 copper pennies. Jenna has a large container of pennies at home. She selects a random sample of 50 pennies from the container and finds that 11 are pre-1982 copper pennies Does this provide convincing evidence that the proportion of pennies in her container that are pre-1982 copper pennies is greater than 0.132?
a. Identify the population, parameter, sample and statistic.
Population:________ parameter_________
Sample_________Statistic:__________
b. Does Jenna have some evidence that more than 13.2% of her pennies are pre-1982 copper pennies?
c. Provide two explanations for the evidence described in #2.
a)
Population: All pennies in the containerParameter: p = Proportion of pre-1982 copper pennies in the containerSample: 50 randomly selected pennies from the containerStatistic: Number of pre-1982 copper pennies in the sample = 11b) If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is evidence that the proportion is greater than 0.132.
c. Two possible explanations for the evidence that Jenna found are given below.
Solution:
a.
Identify the population, Parameter, sample, and statistic.
Population: All pennies in the container
Parameter: p = Proportion of pre-1982 copper pennies in the container
Sample: 50 randomly selected pennies from the container
Statistic: Number of pre-1982 copper pennies in the sample = 11
b.
To determine if Jenna has convincing evidence that more than 13.2% of her pennies are pre-1982 copper pennies, we can perform a hypothesis test.
Let's assume that the null hypothesis is that the proportion of pre-1982 copper pennies in the container is equal to 0.132, while the alternative hypothesis is that the proportion is greater than 0.132.
Then, we can calculate the test statistic and compare it to the critical value.
If the test statistic is greater than the critical value, we can reject the null hypothesis and conclude that there is evidence that the proportion is greater than 0.132.
c. Two possible explanations for the evidence that Jenna found could be:
1. The container has a higher proportion of pre-1982 copper pennies than the national average.
2. Jenna's sample is not representative of the container, and the sample proportion is higher than the population proportion by chance.
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The daily return of the stock XYZ is normally distributed with a mean of 20 basis points and a standard deviation of 40 basis points. Find the probability of making a gain that amounts for more than one standard deviation from the mean on any given day.
The probability of making a gain that exceeds one standard deviation from the mean for stock XYZ on any given day is approximately 31.73%.
The probability of making a gain that amounts to more than one standard deviation from the mean on any given day for the stock XYZ can be found using the properties of the normal distribution.
To calculate this probability, we need to find the area under the normal distribution curve beyond one standard deviation from the mean in the positive direction. In this case, the mean (μ) is 20 basis points and the standard deviation (σ) is 40 basis points.
Using the standard normal distribution, we can convert the value one standard deviation above the mean (μ + σ) to a z-score by subtracting the mean and dividing by the standard deviation.
Z = (X - μ) / σ
Z = (μ + σ - μ) / σ
Z = σ / σ
Z = 1
Once we have the z-score, we can look up the corresponding probability using a standard normal distribution table or a statistical calculator.
The area under the normal curve beyond one standard deviation from the mean in the positive direction corresponds to approximately 0.1587 or 15.87%.
Therefore, the probability of making a gain that amounts to more than one standard deviation from the mean on any given day for stock XYZ is approximately 0.1587 or 15.87%.
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In a two-way between subjects ANOVA, a significant main effect for B means that
A - the mean for B1 is not equal to the mean for B2.
B - the difference between A1 and A2 is not the same at B1 as for B2.
C - the mean for A1 is equal to the mean for A2.
D - the mean for B1 is equal to the mean for B2.
In a two-way between subjects ANOVA, a significant main effect for B means that option A - the mean for B1 is not equal to the mean for B2.
In a two-way ANOVA, we are examining the effects of two independent variables (factors) on a dependent variable. One of the factors is referred to as factor A, and the other as factor B. A main effect for B indicates that there is a significant difference between the means of the levels of factor B. Therefore, if we observe a significant main effect for B, it implies that the mean for B1 (one level of factor B) is not equal to the mean for B2 (another level of factor B). This suggests that the variable represented by factor B has a significant influence on the dependent variable, and there is a difference in the outcome between the two levels of factor B.
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Sophia drove 63 miles. Sophia's car used 2 gallons of gas. How many miles per gallon did Sophia car get?
Answer:
31.5 mi/gal
Step-by-step explanation:
[tex]63[/tex]÷[tex]2[/tex][tex]=31.5[/tex]
So, Sophia got 31.5 miles per gallon
Answer: 31.5 I think.
Step-by-step explanation:
Give other person brainliest
7.
A customer went to a garden shop and bought some potting soil for $17.50 and 4 shrubs. The total bill was $53.50. Write and solve an equation to find the price of each shrub.
A. 4p + $17.50 = $53.50; p = $9.00
B. 4p + 17.5p = $53.50; p = $2.49
C. 4p + $17.50 = $53.50; p = $11.25
D. 4(p + $17.50) = $53.50; p = $4.00
Answer: A. 4p + $17.50 = $53.50; p = $9.00
1: 17.50+4p= Nothing further can be done with this topic. Please check the expression entered or try another topic.
17.5 + 4 p
2: 4p=53.50-17.50= 4p=53.50-17.50
Step-by-step explanation: 9
The total bill: $53.50
17.50 + 4 x = 53.50
4 x = 53.50 - 17.50
4 x = 36
x = 36 : 4
x = $9
Answer: The price of each shrub is $9.
...............................................................................................................................................
Answer:
$9
Step-by-step explanation:
Let be the price of each shrub.
4 shrubs at each costs dollars
Potting soil is $17.50
Hence, total cost is the expression
We know that total bill is $53.50, so we can equate it to the expression:
This equation can be solved for to find cost of each shrub.
Solving for gives us:
So price of each shrub is $9
Write the word sentence as an equation. 12 less than a number m equals 20.
Answer:
12 - m = 20
Explanation: Less than can also be a subtraction symbol so 12 less than a number, which the number is unknown in this case would be replaced with m then equals to 20. 12 - m =20
find the LCM lowest common multiple and the HCF highest common factor of 40 and 56
Answer:
280 and 8
Step-by-step explanation:
the LCM is the lowest common multiple
the lowest multiple that can Divide 40 and 56 without a remainder = 280
the Hcf Is the highest common factor of 40 and 56
the highest number that can Divide both =8
Answer the following questions about about the arrangements of MILLIMICRON.
1. How many distinguishable ways can the letters of the word MILLIMICRON be arranged in order?
2. How many distinguishable orderings of the letters of MILLIMICRON begin with M and end with N?
3. How many distinguishable orderings of the letters of MILLIMICRON contain the letters CR next to each other in order and also the letters ON next to each other in order?
1. The given word is "MILLIMICRON". The word has 11 letters in total and consists of 2 M's, 2 I's, 2 L's, 1 C, 1 R, 1 O, and 1 N. So, we can use the formula for finding permutations of n objects of which p are of the same kind, q are of another kind, r are of the third kind, and so on. The formula is `n!/(p!q!r!...)`. Here, we have p = 2, q = 2, r = 2, and so on. So, the number of distinguishable ways that the letters of the word "MILLIMICRON" can be arranged in order is: `11!/(2!2!2!) = 4989600` 2. We are given that the distinguishable orderings of the letters of "MILLIMICRON" begin with "M" and end with "N". We have fixed two letters at the beginning and end.
Now, we have 9 letters left which can be rearranged in the remaining 9 spots. So, the number of distinguishable orderings of the letters of "MILLIMICRON" that begin with "M" and end with "N" is: `9!/(2!2!1!) = 22680`3. We are given that the distinguishable orderings of the letters of "MILLIMICRON" must contain the letters "CR" next to each other in order and also the letters "ON" next to each other in order. We can group "CR" and "ON" together as a single letter. So, we have 9 letters: {M, I, L, L, I, M, C, RON, O}. We need to find all the distinguishable orderings of these letters. Let's consider the group "RON" as a single letter. Now, we have 8 letters: {M, I, L, L, I, M, C, RON}. These 8 letters can be arranged in 8! ways. Within the group "RON", we can arrange the letters "R", "O", and "N" in 3! ways. So, the total number of distinguishable orderings of the letters of "MILLIMICRON" that contain the letters "CR" next to each other in order and also the letters "ON" next to each other in order is: `8!×3! = 20,160`.
Hence, the answers are: 1. 4,989,6002. 22,6803. 20,160
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2. Translate the sentence to function notation:
The cost of shipping depends on the distance shipped.
Answer:
see the explanation below
Step-by-step explanation:
The expression for the cost can be given as
y=mx+c
where x= the distance
m= the cost to move x distance
c= the fixed cost
Therefore the total cost to ship the cost will be y
pls HeLp meee and tyy
Answer:
Step-by-step explanation:
El usuario se registra medio de una temperatura de 8 grados centígrados Sin embargo a las 22 horas la temperatura y ha bajado unos 10 grados centígrados Cuál es la temperatura en este momento
Answer:
La temperatura en estos momentos es -2 grados centígrados.
Step-by-step explanation:
Dado que conoces que había una temperatura de 8°C y que a las 22 horas esta ha bajado unos 10 grados, tienes que restar estos 10 grados de la temperatura inicial para saber cuál es la temperatura actual:
8-10=-2
De acuerdo a esto, la respuesta es que la temperatura en estos momentos es -2 grados centígrados.