The correct answer is option (C).
What are the fundamental forms of trigonometry?Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).
The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:
t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)
The vector's magnitude is given by:
|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296
The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.
θ = tan⁻¹ (–9/–5) ≈ 60.945°
In trigonometric form, the vector t is thus represented as follows:
t = [t|cos|i] + [t|sin|j]
We get the following by altering the values of |t| and:
t = 10.296 cos I + 10.296 sin j of angle 60.945
As a result, the following is the proper trigonometric representation of the vector t:
t = 10.296 cos I + 10.296 sin j of angle 60.945
Thus, alternative is the right response (C).
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consider a completely randomized design with k treatments. assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. determine the total number of pairwise comparisons for k.
The total number of pairwise comparisons for k is (k*(k-1))/2.
There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.
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how many square tiles are shaded and not shaded for the 8th figure?
PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, although the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins. About 75 % of Italians can taste PTC. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. (a) Starting with the 75 % estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence? (Enter your answer as a whole number.) n = (b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. (Enter your answer as a whole number.) n =
(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.
(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.
(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²
Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).
n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74
Since we need a whole number, we round up to the nearest whole number:
n = 51
(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):
n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65
Again, rounding up to the nearest whole number:
n = 68
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if the measure of and acute angle is represented by x, then the measure of the angle that it is complementary which is represented by 90-x
The measure of the angle that it is complementary which is represented by 90-x is always true. Option A
What is an acute angle?An acute angle is simply defined as an angle that measures from 90° and 0°. This means that it is smaller than a right angle.
It is formed in the space between two intersecting lines or planes, or from the intersection of two shapes.
What is a complementary angle?A complementary angle can be defined as a pair of angles whose sum is equal or equivalent to 90 degrees.
From the information given, we have that;
x is the acute angle
The complementary angle is 90 - x
We can see that the angle x must be complementary to be subtracted from 90 degrees.
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The complete question:
If the measure of an acute angle is represented by x, then the measure of its complement is represented by 90 – X.
always true
sometimes true
never true
For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
a) Option A, A x2 statistic provides strong evidence in favor alternative hypothesis if its value is a large positive number.
b) Option B, The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related.
c) Option B, The variables considered in a chi-squared test used to evaluate a contingency table B. are categorical.
(a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number. The x2 statistic is used in hypothesis testing to determine whether there is a significant difference between observed and expected frequencies. A large positive value indicates that the observed frequencies are significantly different from the expected frequencies, which supports the alternative hypothesis.
(b) The hypotheses being tested in a chi-squared test on a contingency table are the null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. This test determines whether there is a significant association between two categorical variables.
(c) The variables considered in a chi-squared test used to evaluate a contingency table are categorical. These variables cannot be averaged or assumed to be normally distributed. The chi-squared test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
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if x < y < z and all three are consecutive non-zero integers, then which of the following must be a positive odd integer?
Option (A) x+1 is a positive odd integer.
Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.
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Construct triange ABC, in which AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. Measure the length of BC. Give your answer to 1 d. P
From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm
To construct triangle ABC, we can follow these steps:
Draw a line segment AB of length 6 cm.Draw an angle of 96 degrees at point A using a protractor.Draw an angle of 35 degrees at point B using a protractor.The intersection point of the two lines that were drawn in step 2 and 3 will be point C, which is the third vertex of the triangle.To measure the length of BC in triangle ABC, we can use the law of sines.
The law of sines states that in any triangle ABC:
a / sin(A) = b / sin(B) = c / sin(C)
Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.
In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:
angle ACB = 180 - angle BAC - angle ABC
= 180 - 96 - 35 = 49 degrees
Now, we can apply the law of sines to find the length of BC:
BC / sin(35) = 6 / sin(96)
BC = 6 × sin(35) / sin(96)
Using a calculator, we can evaluate this expression to get:
BC ≈ 4.22 cm
Therefore, the length of BC in triangle ABC is approximately 4.22 cm.
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What is the slope of the line described by the equation below?
y = -6x +3
O A. -6
() в. -з
O C. 6
OD. 3
SUBMIT
Jenny wants to measure the height of a tree she sites the top of the tree using a mirror that is lying flat on the ground. The mirror is 20 feet from the tree, and Jenny is standing 8 feet from the mirror as shown in the figure, her eyes are 5 feet above the ground how tall is the tree?
The Height of tree is around 8.33 feet tall.
What is the connection among Height and distance?In science, we work out the Height of an item utilizing distance and points. Distance is the even distance between the items, and point is the point over the level of the article's top, which gives the item's level.
We can utilize the rule of comparable triangles.
The hypotenuse of this triangle would be the line associating Jenny's eyes to the highest point of the tree (we should refer to this distance as "h").
We can set up the accompanying extent between the two triangles:
h / 20 = (h + 5) / 8
To solve for "h", we can cross-multiply and simplify:
8h = 20(h + 5)
8h = 20h + 100
12h = 100
h = 8.33 feet
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Solve the system of equations:
y = 2x – 5
y = x^2 – 5
A. (–1, –7) and (4, 3)
B. (–1, –4) and (3, 4)
C. (0, –5) and (2, –1)
D. (0, 5) and (2, 2)
Answer:
C. (0, –5) and (2, –1)
The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing (in cm²/s)?
Answer:
Step-by-step explanation: In the problem, they tell us that
dL / dt = 7 cm/s (the rate at which the length is changing) and
dw / dt = 8 cm/s (the rate at which the width is changing)
Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm
The equation for the area of a rectangle is:
A = L·w, so will need the product rule when taking the derivative.
dA/dt = L (dw/dt) + w (dL/dt)
Now just plug in all of the given numbers:
dA/dt = (7)(7) + (5)(8) = 49+40 = 89 cm²/s
Let Y be a binomial random variable with n trials and probability of success given by p. Use the method of moment-generating functions to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p.
U is a binomial random variable with n trials and probability of success given by 1 - p.
As Y is a binomial random variable with n trials and probability of success given by p. Using the moment-generating functions method, it can be shown that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The binomial distribution is described by two parameters: n, which is the number of trials, and p, which is the probability of success in any given trial. If a binomial random variable is denoted by Y, then:[tex]P(Y = k) = \binom{n}{k}p^{k}(1 - p)^{n-k}[/tex]
The method of generating moments can be used to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The moment-generating function of a binomial random variable is given by: [tex]M_{y}(t) = [1 - p + pe^{t}]^{n}[/tex]
The moment-generating function for U is: [tex]M_{u}(t) = E(e^{tu}) = E(e^{t(n-y)})[/tex]
Using the definition of moment-generating functions, we can write: [tex]M_{u}(t) = E(e^{t(n-y)})$$$$= \sum_{y=0}^{n} e^{t(n-y)} \binom{n}{y} p^{y} (1-p)^{n-y}[/tex]
Taking the summation of the above expression: [tex]= \sum_{y=0}^{n} e^{tn} e^{-ty} \binom{n}{y} p^{y} (1-p)^{n-y}$$$$= e^{tn} \sum_{y=0}^{n} \binom{n}{y} (pe^{-t})^{y} [(1-p)^{n-y}]^{1}$$$$= e^{tn} (pe^{-t} + 1 - p)^{n}[/tex]
Comparing this expression with the moment-generating function for a binomial random variable, we can say that U is a binomial random variable with n trials and probability of success given by 1 - p.
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a 20-volt electromotive force is applied to an lr-series circuit in which the inductance is 0.1 henry and the resistance is 40 ohms. find the current i(t) if i(0) = 0.
i(t) = ___
Determine the current as t → [infinity].
lim t→[infinity] i(t) =_____
The time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
The current of the given LR-series circuit can be determined using the formula I = (E/R) * (1 - e^-Rt/L).The current i(t) if i(0) = 0 in the LR-series circuit is given by i(t) = 0.125A. The current as t → [infinity] is given by lim t→[infinity] i(t) = 0.How to solve this?The formula for the current in the LR-series circuit is given by:Where E is the electromotive force, R is the resistance, L is the inductance, t is time and I is the current.I = (E/R) * (1 - e^-Rt/L)Given E = 20V, R = 40Ω, L = 0.1H, and i(0) = 0Substitute these values in the above formula.I = (20/40) * (1 - e^-40t/0.1)I = 0.5(1 - e^-400t)I = 0.5 - 0.5e^-400tSo the current is i(t) = 0.5 - 0.5e^-400t.Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0. Answer: The current is i(t) = 0.5 - 0.5e^-400t. Limit of t as t → [infinity] means that when the time is allowed to run infinitely, then the current will become constant. Hence, when the time becomes infinity, i(t) will become constant, i.e., lim t→[infinity] i(t) = 0.
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1. Find the given derivative by finding the first few derivatives and observing the pattern that occurs. (d115/dx115(sin(x)). 2. For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a comma- separated list.) f(x) = x + 2 sin(x).
The values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
1. The given derivative can be found by finding the first few derivatives and observing the pattern that occurs as shown below;Differentiating sin x with respect to x gives the derivative cos x. Continuing this process, the pattern that emerges is that sin x changes sign for every odd derivative, and stays the same for every even derivative. Therefore the 115th derivative of sin x can be expressed as follows;(d115/dx115)(sin x) = sin x, for n = 58 (where n is an even number)2. To find the values of x such that the graph of f has a horizontal tangent, we differentiate f with respect to x, and then solve for x such that the derivative equals zero. We have;f(x) = x + 2sin xDifferentiating f(x) with respect to x gives;f'(x) = 1 + 2cos xFor a horizontal tangent, f'(x) = 0, thus;1 + 2cos x = 02cos x = -1cos x = -1/2The solutions of the equation cos x = -1/2 are;x = 2π/3 + 2πn or x = 4π/3 + 2πnwhere n is an integer. Therefore the values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
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The accurate scale diagram shows a telephone mast and a box.
Find an estimate for the real height, in metres, of the telephone mast.
telephone mast
5.5
+2.5 m
box
+
Total marks: 2
Using proportions, the real height of the telephone mast is estimated to be 9 meters.
What exactly is a proportion?A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.
The following proportional relationship is established as a result:
x / 1.5 cm = 10.8 cm / 1.8 cm.
The relationship's left side can be simplified as follows:
6 = x / 1.5 cm.
The estimate is then calculated using cross multiplication, as shown below:
6 x 1.5 cm = 9.5 cm².
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Six more than the quotient of a number and 8 is equal to 4
use the variable x for the unknown number
!!!TRANSLATE INTO A EQUATION!!!
Answer:
x/8 + 6 = 4
Step-by-step explanation:
x / 8 + 6 = 4
x/8 = -2
x = 8*-2 = -16.
which sampling approach was used in the following statement?kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in wisconsin to study their attitudes toward evidence-based practice.
The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.
What is Stratified random sampling?Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.
Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.
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when an automatic press is a manufacturing process is operaing properly, the lengths of the component it produces are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches. what is the probability thata randomly selected component is shorter than 7 inches long? (report your answer to 4 decimal places.)
The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.
What is the probability of randomly selected component?We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.
We need to find the probability that a randomly selected component is shorter than 7 inches long.
We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:
z = (7 - 8) / 1.5 = -0.67
Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:
P(z < -0.67) = 0.2514
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stuck on this question need some help
Answer:
1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).
2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).
3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).
The hanger image below represents a balanced equation.
Write an equation to represent the image
HELP THIS IS DUE TODAY
Answer:
2 + r = 6
Step-by-step explanation:
2 + r = 6
r = 6 - 2 = 4
6 on the left balanced by 2 plus r on the right
the probability that deshawn palys basketball after school is 20% the probability that he talks to friends after school is 45% he says the p b or t is 65% explain dans error
Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
How do we find the error?Given:
Probability of Deshawn playing basketball after school = 20%Probability of Deshawn talking to friends after school = 45%Probability of Deshawn doing either basketball or talking to friends after school = 65%Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%
Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%
The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.
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Maria purchased 1,000 shares of stock for $35. 50 per share in 2014. She sold them in 2016 for $55. 10 per share. Express her capital gain as a percent, rounded to the nearest tenth of a percent
Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.
To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.
The purchase price for 1,000 shares of stock was:
$35.50 x 1,000 = $35,500
The selling price for 1,000 shares of stock was:
$55.10 x 1,000 = $55,100
The capital gain is the difference between the selling price and the purchase price:
$55,100 - $35,500 = $19,600
To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:
($19,600 / $35,500) x 100 = 55.21%
In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.
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7) Roy buys pizza for his friends. A whole pizza costs P 190. 00 and P 40. 00 for every
additional topping. If he spent P 1070 for pizza with 3 sets of additional toppings, how
many whole pizzas did he buy?
Roy purchased whole pizzas for P 190.00 each. To determine the number of whole pizzas he bought, we can divide the total cost of the pizzas by the cost of each pizza. Therefore, the calculation P 950.00 / P 190.00 results in 5, indicating that Roy bought five whole pizzas.
Roy spent a total of P 1070 for pizza with 3 sets of additional toppings. Since each set of additional toppings costs P 40.00, then the total cost of the toppings is 3 x P 40.00 = P 120.00. Subtracting this from the total amount spent gives us P 950.00, which is the cost of the pizzas alone.
Since each whole pizza costs P 190.00, we can divide the cost of the pizzas by the cost of each pizza to find the number of whole pizzas Roy bought. Therefore, P 950.00 / P 190.00 = 5.
Thus, Roy bought 5 whole pizzas.
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Kate is x years old. Lethna is 3 times as old as Kate. Mike is 4 years older than Lethna. write down an expression, in terms of x for Mike's age
Answer: Mike is ( 3x + 4 ) years old
Step-by-step explanation:
K -> x y/o
L -> 3x y/o
M -> (3x + 4) y/o
10) Find the vertex form of the parabola.
Step-by-step explanation:
4x + y^2 + 2y = - 5
4x = - y^2 -2y - 5
4x = - (y^2 + 2y) - 5 'complete the square' for y
4x = - ( y +1)^2 + 1 - 5
x = - 1/4 ( y+1)^2 - 1 vertex is at -1, -1
-14x+2y^2-8y -20 = 0
14x = 2y^2 -8y-20
14x = 2 ( y^2 - 4y) - 20 complete the square for y
14x = 2(y-2)^2 -8 - 20
x = 1/7 ( y-2)^2 - 2 Vertex is at -2 , 2
please help me !!!!!!
The equation representing total fraction strip is ³/₃ + ¹/₃ = ⁴/₃.
option B.
What is a fraction?
A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.
For this case, 1 is divided into, and 1 divide into 3.
To obtain the total fractions, we will add the individual fractions as shown below;
For this first fraction = ¹/₃ + ¹/₃ + ¹/₃
For the second fraction = ¹/₃
Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃
Total fraction = ³/₃ + ¹/₃ = ⁴/₃
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Please help it’s for tmr, I only have 18 minutes left
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Leo might therefore have 36 or 48 toy soldiers, which is a choice between the two numbers.
What is the greatest number that is possible?The attempt to demonstrate that your integer is larger than anyone else's integer has persisted through the ages, despite their being more numbers than there are atoms in the universe. The largest number that is frequently used is a googolplex (10googol), which equals 101¹⁰⁰.
We'll name Leo's collection of toy soldiers "x" the amount. We are aware of:
We can infer x to be one of the following figures from the first condition: 28, 32, 36, 40, 44, 48, or 52.
To find out which of these integers meets the other two requirements, we can try each one individually:
x + 6 = 34 and x + 3 = 31, neither of which is a multiple of five, if x = 28.
X + 6 = 38 and X + 3 = 35, none of which is a multiple of 5, follow if x = 32.
When x = 36, x + 6 = 42, a multiple of 7, and x + 3 = 39, a multiple of 5, follow. This might be the answer.
x + 6 = 46 and x + 3 = 43, neither of which is a multiple of five, if x = 40.
x + 6 = 50 and x + 3 = 47, neither of which is a multiple of five, if x = 44.
When x = 48, x + 6 = 54, a multiple of 7, and x + 3 = 51, a multiple of 5, follow.
x + 6 = 58 and x + 3 = 55, neither of which is a multiple of five, if x = 52.
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Determine whether the set StartSet left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 0 3rd Row 1st Column negative 3 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 3 2nd Row 1st Column 1 3rd Row 1st Column 6 EndMatrix right bracket comma left bracket Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column negative 1 3rd Row 1st Column 0 EndMatrix right bracket EndSet 1 0 −3 , −3 1 6 , 1 −1 0 is a basis for set of real numbers R cubedℝ3. If the set is not a basis, determine whether the set is linearly independent and whether the set spans set of real numbers R cubedℝ3. Which of the following describe the set?
The set [1 0 −3 , −3 1 6 , 1 −1 0] is not a basis for set of real numbers R cubed(ℝ3).
The reason why it is not a basis is because it is not linearly independent. However, the set does span set of real numbers R cubed(ℝ3).To determine if the given set is a basis for set of real numbers R cubed(ℝ3), we need to test for linear independence and for span.Linear independence
The given set is said to be linearly independent if and only if the only solution to the equation a[1 0 −3] + b[−3 1 6] + c[1 −1 0] = [0 0 0] is the trivial solution where a, b and c are constants.If the given set is linearly independent then it is a basis for R3; if it is not linearly independent, it is not a basis for R3.
SpanThe given set is said to span R3 if every vector in R3 can be written as a linear combination of vectors in the given set.
If the given set spans R3, then it can be considered a basis for R3.For us to test if the given set is linearly independent, we can form a matrix by placing the three given vectors into the columns of a 3 x 3 matrix as follows:[1 0 1] [−3 1 −1] [−3 6 0]
By expanding the determinant of the matrix above, we get: det(A) = 0 - 0 - (-3) = 3
Since the determinant is non-zero, we can say that the given set is linearly independent. Since the given set is linearly independent, we can then use it to span R3. Hence the given set does not form a basis for R3 but it is linearly independent and spans R3.
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Question
The average of three numbers is 16. If one of the numbers is 18, what is the sum of the other two
numbers?
12
14
20
30
If the average of three numbers is 16 and one of the numbers is 18, then the sum of the other two numbers is option (d) 30
Let's use algebra to solve this problem. Let x and y be the other two numbers we are looking for. We know that the average of the three numbers is 16, so we can write:
(18 + x + y) / 3 = 16
Multiplying both sides by 3, we get,
[(18 + x + y) / 3] × 3 = 16 ×3
18 + x + y = 48
Subtracting 18 from both sides, we get,
18 + x + y - 18 = 48
x + y = 30
Therefore, the correct option is (d) 30
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Factorise fully - 4x² - 16x
Answer: 4x(x - 4)
Step-by-step explanation:
4x² - 16x = 4x(x - 4)
Now we can see that the expression inside the parentheses can also be factored:
x - 4 = (x - 4)
So the fully factorized expression is:
4x² - 16x = 4x(x - 4) = 4x(x - 4)
Answer:
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- 4x( x + 4 )
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Step-by-step explanation:
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[tex]\large{\pmb{\sf{ - 4x^{2} - 16x}}}[/tex]
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[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{4}} \: As \: Common:-}}}}[/tex]
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[tex]\large{\pmb{\sf{\leadsto{- 4(x^{2} + 4x)}}}}[/tex]
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[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{x}} \: As \: Common:-}}}}[/tex]
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[tex]\large{\purple{\boxed{\pmb{\sf{\leadsto{- 4x(x + 4)}}}}}}[/tex]
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[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]
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[tex]\large{\dashrightarrow}[/tex] Two positive always makes positive sign when multiplied.
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[tex]\large{\dashrightarrow}[/tex] Two negatives always makes positive sign when multiplied.
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[tex]\large{\dashrightarrow}[/tex] A positive and a negative always makes negative sign when multiplied.
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[tex]\large{\dashrightarrow}[/tex] The sum of two positives is always positive with a positive sign.
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[tex]\large{\dashrightarrow}[/tex] The sum of two negatives is always positive with a negative sign.
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[tex]\large{\dashrightarrow}[/tex] The sum of a positive and a negative is always negative with the sign of whose number is greater.
