Given that √7 is a solution to the equation x² = 7, we can use this equation to find a decimal approximation of √7 that satisfies the given condition.
First, we can estimate that √7 is between 2.5 and 3, since 2² = 4 < 7 and 3² = 9 > 7.
Next, we can try using a decimal approximation of √7, such as 2.6 or 2.7, and square it to see if the result is between 6.9 and 7.1.
If we try 2.6, we get:
(2.6)² = 6.76
Since this is less than 6.9, we can try a larger value, such as 2.7:
(2.7)² = 7.29
Since this is greater than 7.1, we can try a value between 2.6 and 2.7, such as 2.65:
(2.65)² = 7.0225
This result is between 6.9 and 7.1, so a decimal approximation of √7 that satisfies the given condition is approximately 2.65.
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Two chords: help Find x
The value of x in the given figure on the basis of chords intersecting in a circle at an anle of 65° and the intercepted arcs being (4x) and (2x+10) is 20.
What is chord?
A chord is a line segment which joins any two points on the circle. If the line segment joins two end points and also passes through the circle then it would be the largest chord which is also called as the diameter. The chord divides the circle into two parts namely the major segment & minor segment.
Here two chords intersect inside the circle at 65° and the measure of the intercepted arcs are given as (4x)° and (2x+10)°
As per the thoerem of circles, the angle of intersection of chords is equal to half of the sum of the values of intercepted arcs.
Angle of intersection= [tex]\frac{1}{2}[/tex] (sum of intercepted arcs)
65° = [tex]\frac{1}{2}[/tex] (sum of (4x)° and (2x+10)°)
65° = [tex]\frac{1}{2}[/tex] ((4x)° + (2x+10)°)
65° = [tex]\frac{1}{2}[/tex] (4x + 2x+10)
65° = [tex]\frac{1}{2}[/tex] (6x+10)
2 (65°) = (6x+10)
130 = 6x + 10
120 = 6x
x = 20
The value of x = 20
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a random variable x is characterized by a normal probability density function with known mean 20. there are two hypotheses for the variance. hypothesis h0 claims the variance is 16 while hypothesis h1 claims the variance is 25. we will choose between these hypotheses by observing three sample values x1, x2, and x3 and applying a threshold rule of the form reject h0 if x1 x2 x3 > t. for some scalar t. determine the value of t so that the probability of false rejection is 0.05. what is the corresponding probability of false acceptance? your answers should be in terms of the q function. 1
The value of the threshold t that gives a false rejection rate of 0.05 is found to be 5.991. The corresponding probability of false acceptance, or type II error, is computed using the power function of the test and found to be approximately 0.1485.
This is the probability of failing to reject the null hypothesis when the alternative hypothesis is true and the variance is 25.
To determine the value of t that gives a probability of false rejection of 0.05, we need to find the distribution of the test statistic under the null hypothesis H0: σ^2 = 16. The test statistic is:
T = (X1 - μ)² + (X2 - μ)² + (X3 - μ)² / (nσ²)
Under the null hypothesis, T follows a chi-squared distribution with 2 degrees of freedom (n-1). We can use this distribution to find the value of t such that the probability of false rejection is 0.05.
From the tables of the chi-squared distribution, we find that the critical value of T for a false rejection rate of 0.05 is 5.991.
Thus, we reject the null hypothesis if T > 5.991.
The probability of false acceptance, also known as type II error, is the probability of failing to reject the null hypothesis when it is actually false (i.e., when H1: σ^2 = 25 is true). This probability depends on the value of σ^2 and the threshold t.
To find the probability of false acceptance, we need to compute the power of the test, which is the probability of rejecting the null hypothesis when it is false. The power function is given by:
β(σ²) = P(T > t | σ² = 25)
The distribution of T under H1 is also a chi-squared distribution with 2 degrees of freedom, but with a different scale parameter:
T ~ χ^2(2, nσ^2/25)
Using the non-central chi-squared distribution, we can compute the power function:
β(σ²) = Q(√(n/25)(t - 3.2), 2, δ)
where Q is the complementary cumulative distribution function (CCDF) of the non-central chi-squared distribution, δ = √(n)(20-25)/5, and t is the threshold value.
For t = 5.991, we have:
[tex]δ = √(3)(20-25)/5 = -1.3416\\\\β(16) = Q(√(3/25)(5.991 - 3.2), 2, -1.3416) ≈ 0.1485\\β(25) = Q(√(3/25)(5.991 - 3.2), 2, 0) ≈ 0.4259[/tex]
Therefore, the probability of false acceptance is
P(accept H1 | H1 is false) = β(16) ≈ 0.1485
Note that this is the probability of failing to reject H0 when H1 is true and σ^2 = 25. It is not the probability of accepting H1 when H0 is true and σ^2 = 16, which is 1 - the probability of false rejection.
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Find the area of the shaded region. Round your answer to the nearest hundredth.
Help ASAP please!!!
Check the picture below.
so hmmm the square inscribed in the circle, we can see it as two congruent triangles, whose base is 28 and height is 14. Now, if we get the whole area of the circle with radius of 14, and subtract the area of those triangles, what's leftover is the shaded area.
[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ circle }{\pi (14)^2}~~ - ~~\stackrel{ \textit{two triangles} }{2\left[\cfrac{1}{2}(\underset{b}{28})(\underset{h}{14}) \right]}}\implies 196\pi -392 ~~ \approx ~~ \text{\LARGE 223.75}[/tex]
is alice looking at a region of maximum brightness, minimum brightness, or neither? explain your reasoning.
As Alice looks at the color spectrum, she is looking at a region of maximum brightness.
Alice is looking at a region of maximum brightness because when we observe the color spectrum, we can see that the rainbow's center is the brightest, and the intensity of light at this location is the highest. Red color has the lowest energy, followed by orange, yellow, green, blue, indigo, and violet. It can be observed from the color spectrum that red has the lowest energy, followed by orange, yellow, green, blue, indigo, and violet.
White light can be separated into several colors in the color spectrum. The highest energy level is found in violet, whereas the lowest energy level is found in red. As Alice looks at the color spectrum, she is looking at a region of maximum brightness.
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Select the correct answer. The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation: 2n + 1 = 157. What is the first number? A. 77 B. 78 C. 79 D. 80
With the help of given expression 2n + 1 = 157, the first number is 78.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, symbols, and operators that represent a value. It can be a single term, or it can be a combination of terms connected by operators. For example, 2x + 5 is an expression with two terms connected by the operator +. Expressions can also include functions, variables, and constants.
Now,
Let's assume the first number be x=n. Then the next consecutive number will be x+1.
According to the given information, the sum of the two consecutive numbers is 157.
So, we can write the equation as:
x + (x+1) = 157
Simplifying the equation, we get:
2x + 1 = 157
Subtracting 1 from both sides, we get:
2x = 156
Dividing both sides by 2, we get:
x = 78
i.e. n=78
Therefore, the first number is 78.
So, the correct answer is B) 78.
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the sum of -3 and it's opposite
Answer:
it equals 0
Step-by-step explanation:
3 + -3=0
one of the two linear equations in a system is given. the system has exactly one solution. which equation could be the second equation in this system?
The second equation in the system could be 2y - 1/x = 7
We know that the given equation is
y = 1/x + 5
If the system has no solution, then the second equation must be inconsistent with the given equation. In other words, the two equations must represent two lines that do not intersect.
To find such an equation, we need to look for a linear equation that cannot be satisfied simultaneously with y = 1/x + 5. One such equation could be
2y - 1/x = 7
To see why this equation is inconsistent with y = 1/x + 5, let's try to solve the system formed by these two equations
y = 1/x + 5 (equation 1)
2y - 1/x = 7 (equation 2)
Multiplying equation 1 by 2, we get
2y = 2/x + 10
Substituting this into equation 2, we get
2/x + 10 - 1/x = 7
Simplifying this equation, we get
1/x = -3
But this equation has no solution, because there is no value of x that can make 1/x equal to -3. Therefore, the system formed by equations 1 and 2 has no solution.
The second equation is
2y - 1/x = 7
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The given question is incomplete, the complete question is:
y = 1/x + 5
One of the two equations in a linear system is given. The system has no solution. Which equation could be the second equation in this system?
I need Helpppp my teacher sucks at teaching
The missing value in the given figure is 120 degree.
What is an isosceles trapezoid?An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent.
What is angle theorem of trapezoid?The base angles of an isosceles trapezoid are congruent.
The converse is also true: If a trapezoid has congruent base angles, then it is an isosceles trapezoid.
Equation:In CFED,
As it is and isosceles trapezoid,
m∠C=m∠F
m∠D=m∠E
∴m∠F = 60 degrees
Now
m∠D+m∠E+m∠F+m∠C = 360 degree
2m∠D+120=360
m∠D=(360-120)/2
∴m∠D=120 degree
Thus the value of missing angle is 120 degree.
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(−5,5), B(−1,1), C(6,5), D(6,−3), E(−5,−3)
The area of the first triangle formed by points A, E, and B is 16 square units, the second triangle is formed by points B, C, and D, and the pentagon is formed by points B, C, and D the given points are 30 square units.
To plot and connect the given points in order, we first arrange them in a clockwise direction starting from point A(-5, 5).
The order is A, E, D, C, B, and A.
The rectangle is formed by the points C, D, and their respective y-coordinates. The length of the rectangle is 6 - 6 = 0 units, and the width is 5 - (-3) = 8 units.
The first triangle is formed by points A, E, and B. The base of the triangle is 4 units (the x-coordinate of E minus the x-coordinate of A), and the height is 8 units (the y-coordinate of A minus the y-coordinate of E).
The second triangle is formed by the points B, C, and D. The base of the triangle is 7 units (the x-coordinate of C minus the x-coordinate of B), and the height is 4 units (the y-coordinate of B minus the y-coordinate of D).
Therefore, the area of the rectangle is:
0 x 8 = 0 square units.
The area of the first triangle is:
0.5 x 4 x 8 = 16 square units.
The area of the second triangle is:
0.5 x 7 x 4 = 14 square units.
The total area of the pentagon is:
area of the rectangle + area of the first triangle + area of the second triangle
16 + 14 + 0 = 30 square units.
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Earl selects 8 toy cars to bring to show and tell at his daycare. These cars make up 40% of Earl's total toy car collection. What is the total number of toy cars that Earl owns?
Enter the correct number in the box.
_____
Answer:
20 cars
Step-by-step explanation:
.4x = 8
x = 20 cars
To verify the answer, 40% of 20 is 8.
The volume of a sphere is 2,143.57 yd³. To the nearest yard, what is the radius of the sphere? Use 3.14 for .
The radius of the sphere is about yd.
The radius of the sphere is about 8 yards.
Calculating the radius of the sphereThe formula for the volume of a sphere is V = (4/3)πr³, where V is the volume, r is the radius, and π is the mathematical constant pi, approximately equal to 3.14.
We can rearrange the formula to solve for the radius:
r = ((3V)/(4π))^(1/3)
Substituting the given volume V = 2,143.57 yd³ and π = 3.14, we get:
r = ((3 x 2,143.57)/(4 x 3.14))^(1/3)
Evaluate
r ≈ 8.0
Rounding to the nearest yard, the radius of the sphere is approximately 8 yards.
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Solve for y and x. (use the POSITIVE value of y)
Blank 1: y
Blank 2: x
Therefore, the sides of the two triangles for x = 2 are approximately 106.099 and 22.317. After a few iterations, we get an approximate value of y for x = 2: y_1 = 9.618, y_2 = 9.614 and y_3 = 9.614
What is triangle?A triangle is a two-dimensional geometrical shape with three straight sides and three angles. It is one of the basic shapes in geometry and is commonly encountered in mathematics, science, and everyday life. Triangles can be classified based on the lengths of their sides and the measures of their angles. Some common types of triangles include equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), and scalene triangles (no sides or angles are equal). Triangles have many properties and relationships that are useful in solving problems involving angles, sides, and area.
Here,
Since the two triangles are similar and one triangle is inscribed in the other, the corresponding sides of the two triangles are proportional. That is,
(y² + 16) / (yx² + 9x) = (x² + 7x + y/2) / (3y/2 + 17)
Cross-multiplying and simplifying, we get:
(y² + 16)(3y/2 + 17) = (yx² + 9x)(x² + 7x + y/2)
Expanding and rearranging, we get a quadratic equation in y:
3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836 = 0
This equation is difficult to solve explicitly for y, but we can use numerical methods or algebraic software to find an approximate value of y for a given value of x.
For example, let's assume x = 2. Using a numerical method such as Newton-Raphson, we can iteratively solve for y:
Let f(y) = 3y³ + 44y² + 102y - 816x³ - 5652x² - 7569x - 1836
Let f'(y) be the derivative of f(y): f'(y) = 9y² + 88y + 102
Let y_0 be an initial guess for y, such as y_0 = 10 (any positive value of y would work as an initial guess)
Iterate using the formula: y_n+1 = y_n - f(y_n) / f'(y_n), starting with n = 0
After a few iterations, we get an approximate value of y for x = 2:
y_1 = 9.618
y_2 = 9.614
y_3 = 9.614
Therefore, for x = 2, the positive value of y is approximately 9.614. We can then use this value to find the corresponding sides of the two triangles:
Side of big triangle: y² + 16
= 9.614² + 16
= 106.099
Side of small triangle: x² + 7x + y/2
= 2² + 7(2) + 9.614/2
= 22.317
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(i) Find a formula for the total cost $T of c pens at $d each and e pencils at f cents each.
Step-by-step explanation:
The total cost of c pens is $cd. The total cost of e pencils is $0.01ef. Thus, the formula for the total cost is:
$T = cd + 0.01ef
ted claims that the two shaded triangles must be congruent. is ted's claim correct? include all work
and/or reasoning necessary to either prove the triangles congruent or to disprove ted's claim.
Ted's claim is correct - the two shaded triangles must be congruent.
We can prove this using the following reasoning:
The two triangles share the same base, segment BC.
The two triangles have the same height, as the height of a triangle is measured as a perpendicular line from the base to the opposite vertex, and the perpendicular line from B to segment AD is the same length as the perpendicular line from C to segment AE.
Therefore, the two triangles have the same area.
If two triangles have the same area and share a common side (in this case, segment BC), they must be congruent by the Side-Area-Side (SAS) congruence theorem.
Therefore, we can conclude that the two shaded triangles are congruent.
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Evaluate the definite integral. Use a graphing utility to verify your result.
The value of the definite integral is -28/3
How to evaluate the definite integralUsing the power rule of integration, we can find the antiderivative of t^2 - 5 as follows:
∫(t^2 - 5) dt = (1/3)t^3 - 5t + C
where C is the constant of integration.
To evaluate the definite integral, we substitute the limits of integration into this expression and take the difference:
∫^-1_1 (t^2 - 5) dt = [(1/3)(1^3) - 5(1)] - [(1/3)(-1^3) - 5(-1)]
= (1/3 - 5) - (1/3 + 5)
= (-14/3) (16/3)
= -28/3
Therefore, the value of the definite integral is -28/3.
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pls help soon I need this asap
Answer:
QPS=110
m<2= 55
m<7=35
m<3=35
m<PQR=70
Step-by-step explanation:
the two lines interesting the rhombus were perfectly cut in half
HELP ! find the unit price for a 16-oz, jar of peanut butter for $3.28
Step-by-step explanation:
$ 3.28 / 16 oz = $ .205 per ounce which rounds to 21 cents per ounce
a pound of popcorn is popped for a class party. the popped corn is put into small popcorn boxes that each hold popped kernels. there are kernels in a pound of unpopped popcorn. if all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last partially filled box?
There are a total of 36 boxes of popcorn with each box containing 2 popped kernels except for the last box which contains 1 popped kernel.
If there are 85 kernels in a pound of popcorn, then we can assume that there are 84 boxes of popcorn with each box containing one kernel less than the previous box. The last box will contain only one kernel.
Following formula should be used to find the sum of the first n natural numbers:
n(n+1)/2.
Therefore, the number of boxes required to hold all the popped kernels is given by solving the equation:
n(n+1)/2 = 84
Solutions for the quadratic equation can be found as:
n = -9 or n = 8
Since we cannot have a negative number of boxes, therefore, we take:
n = 8.
Therefore, there are a total of 36 boxes of popcorn with each box containing 2 popped kernels except for the last box which contains 1 popped kernel.
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The number of boxes required for the popped corn can be calculated by dividing the total number of popped kernels by the capacity of each box. To do this, we need to know the yield of the popcorn, which means the ratio of popped kernels to unpopped kernels.
Let's assume that the yield of the popcorn is 10:1, which means that for every 10 unpopped kernels, 1 kernel pops. Therefore, there would be 10 x 16 = 160 unpopped kernels in a pound of popcorn.
Assuming that each box can hold 100 popped kernels, we can calculate the total number of boxes required as follows: Total number of popped kernels = 1 lb of popcorn x 10 (yield) = 1600 popped kernels Number of boxes required = 1600 popped kernels ÷ 100 kernels per box = 16 boxes
Therefore, 16 boxes are needed to hold all the popped kernels. The last box will be partially filled, and the number of popped kernels in it can be calculated by subtracting the number of kernels in the other 15 boxes from the total number of popped kernels:
Number of kernels in the last box = 1600 popped kernels - (15 boxes x 100 kernels per box) = 100 popped kernels Hence, there are 16 boxes required to hold all the popped kernels, with the last box having 100 popped kernels in it.
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Solve the inequality
x^2-2x<35
From the sign chart, we can see that the solution set is x < -5 or -5 < x < 7. Therefore, the solution to the original inequality is:
x < -5 or -5 < x < 7
How to solve inequality?In order to solve an inequality, you need to isolate the variable on one side of the inequality symbol (i.e., <, >, ≤, ≥) and determine the range of values for which the inequality holds true.
The process for solving an inequality depends on the specific type of inequality. Here are the general steps for solving different types of inequalities:
Solving linear inequalities:
a. Move all variable terms to one side of the inequality and all constant terms to the other side.
b. Divide or multiply both sides by a positive constant (i.e. not zero) to isolate the variable.
c. If you multiply or divide by a negative constant, flip the inequality symbol to maintain the inequality.
Solving quadratic inequalities:So, the inequality can be written as:
[tex](x - 7) (x + 5) < 0[/tex]
To solve this inequality, we need to consider the sign of the expression on the left-hand side for different values of x. We can do this by creating a sign table:
x | x - 7 | x + 5 | (x - 7) (x + 5)
----------|-----------|-----------|----------------
-6 | -13 | -1 | +13
-4 | -11 | +1 | -11
-1 | -8 | +4 | -32
6 | -1 | +11 | -11
8 | +1 | +13 | +13
From the sign table, we can see that the expression (x - 7)(x + 5) is negative (i.e., less than zero) for values of x between -5 and 7. Therefore, the solution to the inequality is:
[tex]-5 < x < 7[/tex]
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part 2. design the interior girder supporting the ends of joists [which attach on both sides of the girder] from part 1. how many 2x12s does this girder need to span 12 feet?
A single 2 x 12 may suffice to span 12 feet for light residential loads, but it is crucial to verify this with local building codes and a structural engineer for your specific situation.
To design the interior girder supporting the ends of joists from part 1, we need to follow these steps:
Step 1: Determine the load on the girder
First, we need to find out the total load on the girder.
Assuming the joists are evenly spaced and have equal load, we can calculate the total load on the girder.
Step 2: Select the appropriate size of lumber for the girder
For this question, we are asked to use 2 x 12 lumber for the girder.
A 2 x 12 has a nominal size of 1.5 inches x 11.25 inches.
Step 3: Calculate the required number of 2 x 12s for the girder
To determine how many 2 x 12s are needed to span the 12 feet, we need to consider the strength and stiffness of the girder. To do this, we can refer to span tables or consult a structural engineer.
Based on typical span tables, a single 2x12 can span approximately 12 feet for light residential loads.
However, it is essential to consider local building codes and consult a structural engineer to ensure the correct number of 2 x 12s for your specific situation.
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sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one: a. a type i error has been committed b. a one-tailed test has definitely not been used c. the neighborhood is significantly less likely to be democrat d. the difference is not significant
We can conclude that C. the neighborhood is significantly less likely to be Democrat.
The null hypothesis was that there is no difference between the proportion of Democrats in the sample and the population. Since the null hypothesis has been rejected, it means that there is a significant difference between the sample and the population proportions. In this case, 60% of the respondents in the random sample are Democrats, which is lower than the 75% Democrat proportion in the community as a whole. Therefore, we can conclude that the neighborhood from which the sample was drawn is significantly less likely to be Democrat compared to the overall community.
The other options are not supported by the given information:
A type I error might or might not have occurred. We cannot determine this based on the information provided. A type I error refers to the incorrect rejection of a true null hypothesis. Without knowing the true proportions of the neighborhood, we cannot determine if a type I error has been committed. Whether a one-tailed test or a two-tailed test was used is not specified in the question.
However, the conclusion that the neighborhood is significantly less likely to be Democrat can be derived from either type of test. Therefore, the correct option is C.
The question was incomplete, Find the full content below:
sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one:
a. a type i error has been committed
b. a one-tailed test has definitely not been used
c. the neighborhood is significantly less likely to be democrat
d. the difference is not significant
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Because of natural variability in manufacturing, a 16-ounce container of oats does not usually hold exactly 16 ounces of oats. A container is permitted to hold a little more or a little less. The specifications for the oat-filling machine are that it needs to fill each container with 16 ounces of oats with a 2% margin of error. If a container is filled with 16.5 ounces of oats, is the filling machine working within specifications? Explain.
With given expression error=2%, the filling machine is not working within specifications for this container of oats.
What exactly are expressions?
In mathematics, an expression is a combination of symbols, numbers, and operators (such as + and -) that represents a value or a quantity. It can contain variables, which are symbols that represent unspecified values, and constants, which are fixed values. Expressions can be simple, like "5 + 3", or more complex, like "3x² - 2xy + 7".
Now,
The oat-filling machine must fill each container with 16 ounces of oats with a 2% margin of error, according to the requirements. This means that the acceptable range of oat quantity in a container is from 16 - 0.0216 = 15.68 ounces to 16 + 0.0216 = 16.32 ounces.
Since the container in question has been filled with 16.5 ounces of oats, we can see that it is outside the acceptable range specified by the machine's specifications. Therefore, the filling machine is not working within specifications for this container of oats.
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How many times can 3 go into 64
Answer:
How many times can 3 go into 64?
21 times
3 x 21
= 63Step-by-step explanation:
You're welcome.
Answer: 21.3333333333
Step-by-step explanation:
64 / (Divided by) 3 equals 21.3333333...(Recurring, Meaning to go on for infinity)
Simplify the expression: -9 + 4x - 3(x + 2)
Answer: x - 15
Given:
-9 + 4x - 3(x + 2)
Distribute the -3:
-9 + 4x - 3x - 6
Combine similar terms:
-15 + x
Answer:
[tex] \sf \: x - 15[/tex]
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ -9 + 4x - 3(x + 2)
Let's simplify the expression,
→ -9 + 4x - 3(x + 2)
→ -9 + 4x - 3(x) - 3(2)
→ -9 + 4x - 3x - 6
→ 4x - 3x - 9 - 6
→ (4x - 3x) + (-9 - 6)
→ (x) + (-15)
→ x - 15
Hence, the answer is x - 15.
Factor.
2x² + 11x + 12
(x + [?])([ ]x + [])
Enter the number that belongs in the
green box.
Answer:
2x²+11x+12
sum=11x
product =24x²
factor 3x and 8x
2x²+8x+3x+12
2x(x+4)+3(x+4)
(2x+3)(x+4)
What is the value of F
Explain
Hint: use your knowledge of either vertical angles or supplementary angles for this one. Set up an equation and solve for F.
Therefore, the value of F is approximately 18.92 degrees.
What is angle?An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees or radians and can be classified based on their measure as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (between 90 and 180 degrees), or straight (exactly 180 degrees). Angles are an important concept in geometry and have many real-world applications, including in physics, engineering, and architecture.
Here,
If we look at the diagram, we can see that angles d° and e° are vertical angles, which means they are equal in measure. Similarly, angles (9-86)° and 45° are supplementary angles, which means they add up to 180°. Using this information, we can set up an equation:
d = e (since they are vertical angles)
(9-86) + 45 + e + (6f) + 15 = 180 (since the sum of angles in a triangle is 180°)
Simplifying the equation, we get:
-32 + e + 6f + 60 = 180
e + 6f + 28 = 180
e + 6f = 152
Substituting d = e, we get:
d + 6f = 152
But we know that d + e + (9-86) = 180 (since the sum of angles in a straight line is 180°)
Substituting d = e, we get:
2d + (9-86) = 180
2d = 77
d = 38.5
Substituting d = e = 38.5 in the equation e + 6f = 152, we get:
38.5 + 6f = 152
6f = 113.5
f = 18.92
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Find the indefinite integral of:
∫ xsinx^2 (dx)
The indefinite integral of [tex]xsin(x^2)[/tex] with respect to x is [tex]-(1/2)cos(x^2) + C[/tex], where C is the constant of integration.
To evaluate the indefinite integral ∫ [tex]xsinx^2 (dx)[/tex], we used integration by substitution, which is a method for simplifying integrals by substituting a new variable for the original variable.
We can use integration by substitution to evaluate this integral.
Let u = [tex]x^2[/tex], then du/dx = 2x, or equivalently, dx = du/(2x).
Substituting, we have:
∫ [tex]xsinx^2 dx[/tex] = ∫ sin(u) * (du/2)
Now we can integrate with respect to u:
∫ sin(u) * (du/2) = -(1/2)cos(u) + C
We then integrated the resulting expression with respect to u, obtaining -(1/2)cos(u) + C, where C is the constant of integration.
∫ [tex]xsinx^2 dx = -(1/2)cos(x^2) + C[/tex]
Finally, we substituted back u = [tex]x^2[/tex], obtaining [tex]-(1/2)cos(x^2) + C[/tex] as the indefinite integral of [tex]xsinx^2 (dx)[/tex] with respect to x.
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What is the length of one leg of the triangle?
64 cm
64 StartRoot 2 EndRoot cm
128 cm
128 StartRoot 2 EndRoot cm
The length of other leg of the triangle is 64√2 cm.
What is Pythagoras theorem?
For right angle triangle,
Hypotenuse² = Base²+Height ²
Here we have a right angle triangle.
It is given that height and base of the triangle is 8 cm.
Now we want to find other leg of the triangle.
It is clear that other leg means hypotenuse here because this is a right angle triangle.
We know,
Hypotenuse ²= Base²+Height ²
[tex] = {64}^{2} + {64}^{2} \\ = 4096+ 4096 \\ = 2 \times 4096[/tex]
So,
[tex]hypotenuse = \sqrt{2 \times 4096} \\ = \sqrt{64 \times 64 \times2 } \\ = 64\sqrt{2} [/tex]
Therefore, length of the third leg is 64√2 cm.
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Correct question is " There is a right angle triangle. Height and base of the triangle is 8 cm.What is the length of other leg of the triangle?
64 cm
64√2 cm
128 cm
128√2 cm"
a group of 286 students were surveyed about the courses they were taking at their college with the following results: 131 students said they were taking math. 151 students said they were taking english. 158 students said they were taking history. 67 students said they were taking math and english. 55 students said they were taking math and history. 113 students said they were taking english and history. 50 students said they were taking all three courses. how many students took math, english, or history
Using the principle of inclusion-exclusion, 59 students took math only, 21 students took English only, and 40 students took history only.
We can use the principle of inclusion-exclusion to find the number of students who took math, English, or history.
The total number of students who took each course is,
131 (Math) + 151 (English) + 158 (History) = 440
Next, we subtract the number of students taking two courses at a time, since these students have been counted twice in the above totals,
Math and English = 67
Math and History = 55
English and History = 113
We then add back the number of students taking all three courses, since these students have been subtracted twice,
All three courses = 50
Using these values, we can calculate the number of students taking only one course as follows,
Math only = Math - Math and English - Math and History + All three courses = 131 - 67 - 55 + 50 = 59
English only = English - Math and English - English and History + All three courses = 151 - 67 - 113 + 50 = 21
History only = History - Math and History - English and History + All three courses = 158 - 55 - 113 + 50 = 40
Therefore, 59 students took math only, 21 students took English only, and 40 students took history only.
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There are 4 bikes and 12 children what is the ratio of bikes to children
Answer:1:3
Step-by-step explanation:
we can show this as 4:12=1:3
so ratio of bikes to children is 1:3