The first digit in the quotient of 1, 592 64 should be placed in the; Hundredths place.
How to find the quotient with Long division?
When we carry out long division, it is pertinent to note that the first digit of the quotient usually appears over the least significant digit of the very first portion of the dividend that is now greater than or equal to the divisor.
In this question, when we perform long division, we compare;
64 vs 1 . . . no quotient digit
64 vs 15 . . . no quotient digit
64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, with 2 being in the hundredths place.
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If BC = 16.7 ft, what is AY?
Please helpppp
Answer:
16.7
Step-by-step explanation:
YX is similar to AX
XZ is similar to XB
so the triangle AXB is similar to YXZ thus AB is YC
The same goes for the rest of the triangles (YAC and CBZ)
See image attached.
Find the equation of the rational function f whose graph satisfies the conditions horizontal asymptote is y=0 vertical asymptote is x=-3 and contains the point (0,1)
A function assigns the values. The function is f(x) = (8x - 8)/(x² + 2x).
What is a Function?A function transfers each element's value from one set to a particular element in another set.
There is a denominator and a numerator in a rational function.
The x-values that the function approaches but never reaches are known as vertical asymptotes. We can get the vertical asymptotes by setting the denominator to zero.
Since x=-2 and x=0 are the vertical asymptotes, our function's denominator will be x(x+2) = x2+2x.
Y values that the function approaches but never reaches are known as horizontal asymptotes. The degree of the numerator must be less than the degree of the denominator since the horizontal asymptote is y=0. Our numerator will be x - 1 because the x-intercept is equal to 1.
At this time, One can assume that the function is f(x) = (x - 1)/(x2+2x).
Next, we must apply the f(2)=1 condition. If we enter x=2, f(x) ought to be equal to 1. However, we must multiply the function's right side by a constant called C.
Then, the constraint f(2)=1 must be used. F(x) should be equal to 1 if we substitute x=2. The right side of the function must be multiplied by a constant C, though.
1 = C(2 - 1)/(2²+2(2))
Solve for C.
1 = C / 8\s8 = C
Consequently, the equation will be f(x) = [8(x - 1)] / [(x2 + 2x)].
f(x) = (8x - 8) / (x² + 2x)
Thus, f(x) = (8x - 8)/(x2 + 2x) is the function.
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Drag each object to show whether cost is proportional to area in the situation represented.
Increasing the area from 400 to 600 (50%) results in an increase in cost from 500 to 750 (50% increase), which shows that the cost is not proportional to the area.
In a situation where cost is proportional to area, the relationship between cost and area is said to be directly proportional. Direct proportionality means that if the value of one variable (in this case, area) is multiplied by a certain factor, then the other variable (in this case, cost) will also be multiplied by the same factor. The mathematical formula for direct proportionality is [tex]y = kx,[/tex] where y and x are the two variables, and k is the constant of proportionality. If the relationship between the variables is not proportional, then it is a non-proportional relationship.
The objects are proportional if increasing one quantity by a certain factor results in the other quantity increasing by the same factor. In this case, cost is proportional to area if doubling the area would double the cost. Based on the table, we can see that the cost is not proportional to the area since the cost does not increase by the same factor as the area. For example, increasing the area from 400 to 800 (double) results in an increase in cost from 500 to 1000 (also double). However, increasing the area from 400 to 600 (50%) results in an increase in cost from 500 to 750 (50% increase), which shows that the cost is not proportional to the area.
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An employee works at a spin casting machine in a cast iron pipe manufacturing company located
in Charlotte, NC. She has various noise exposures throughout her 8-hour shift. The employee is
currently wearing MSA ear muffs with an NRR of 18 dB.
You have been asked to evaluate her noise exposure and determine if the current hearing protection
provided adequately protects her. You have a type II sound level meter to take noise measurements.
You have set he meter on A scale - slow response. Because the spin casting operation produces wind currents you also are using a wind screen.
After interviewing the employee and taking noise measurements with the sound level meter over the shift you have determined the following about her noise exposures:
95 dBA – for 6 hours while the spin casting machine is spinning
94 dBA – for 1.5 hours while the machine is set up between spins
82 dBA – for 30 minutes while in the lunchroom during breaks
a) What is her TWA noise exposure in dBA over the 8-hour shift?
b) Is the hearing protection adequate?
Answer:
ijsjsjdjdjjejjeks she e nsjksid the Earth travels in around the sun 6.2 Seasonal changes 6.3 Plants and animals are
Step-by-step explanation:
www2 and I 3333333 uth the sun is a bit better now and the Sun 6.2 is better off the moon
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The circle's radius is the same as the radius of the circle whose equation is x2 + y2 = 9.
What is the equation of circle?A circle's standard equation is written as:
x² + y² + 2gx + 2fy + C = 0
The radius of the center is (-g, -f) and radius = √g² + √f² - C
Given a circle with the equation,
x² + y² - 2x - 8 = 0
Find the circle's center.
2gx = -2x
2g = -2
g = -1
Likewise, 2fy = 0.
f = 0
(-(-1), 0) = Centre (1, 0)
This demonstrates that the circle's center is on the x-axis.
r = radius
= √g² + √f² - C
By substituting,
radius = √1² + 0² - (-8)
=√9
= 3 units radius
The circle's radius is three units.
The radius of the circle x² + y² = 9 is written as:
r² = 9
radius = 3 units
As a result, the radius of this circle equals the radius of the circle whose equation is x² + y² = 9.
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Find the nth term of this quadratic sequence
The nth term of the quadratic sequence is aₙ = n² + 2n
What is a quadratic sequence?
Finding the nth term rule of a quadratic sequence: The nth term rule of a quadratic sequence can always be written in the form an² + bn + c.
To find this rule, we need to find a, b and c
Given data ,
Let the expression be represented as = A
Now , the value of A is
A = 3 , 8 , 15 , 24 , 35 ..
Now , taking the difference of the second term and first term , we get
d₁ = 8 - 3 = 5
d₂ = 15 - 8 = 7
d₃ = 24 - 15 = 9
So , the difference of the numbers in the sequence is odd multiples
Therefore , the sequence goes in the multiples of ( n + 2 )
Now , when n = 1
a₁ = 3
when n = 2
a₂ = 8
So , a₂ = n ( n + 2 )
substituting the value for n = 2 , we get
a₂ = 2 ( 2 + 2 )
a₂ = 2 x 4
a₂ = 8
when n = 3
a₃ = 15
So , a₃ = n ( n + 2 )
substituting the value for n = 3 , we get
a₃ = 3 ( 3 + 2 )
a₃ = 3 x 5
a₃ = 15
Therefore , the nth term of the quadratic sequence will be
aₙ = n ( n + 2 )
aₙ = n² + 2n
Therefore , the sequence is aₙ = n² + 2n
Hence , The nth term of the quadratic sequence is aₙ = n² + 2n
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Write the form of the partial fraction decomposition of the function (as in Example 4). Do not determine the numerical values of the coefficients.
The partial fraction decomposition of the function is given as follows:
A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².
How to obtain the partial fraction decomposition of the function?The function in this problem is defined as follows:
(x^4 + x² + 1)/(x²(5x² + 9)²)
Then the partial fraction decomposition is built considering the terms of denominator, as follows:
x².(5x² + 9)².When a term is elevated to a power, the terms with the lower powers also have to be considered. For example, for the denominator x², x is also considered, hence the denominators are given as follows:
x.x².5x² + 9.(5x² + 9)².Then, considering the coefficients A, B, C and D, the partial fraction decomposition of the function is given as follows:
A/x + B/x² + C/(5x² + 9) + D/(5x² + 9)².
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Solve for y: . The solution is blank. The solution is 2(3y-4)=3(y-2/3)
Answer: y=2
Step-by-step explanation:
6y-8=3y-2
3y=6
y=2
How many reflections symmetries does a decagon shaped like a five- pointed star have? How many rotational symmetries does the decagon have? Draw the reflection symmetries on the decagon.
Decagon has a total of 5 reflection symmetries
A reflection symmetry of a shape is a line that divides the shape into two halves that are mirror images of each other. To find the number of reflection symmetries of the decagon, we can draw lines through the center of the decagon that pass through pairs of opposite vertices.
We can draw a total of 5 lines through the center of the decagon that pass through pairs of opposite vertices. Each of these lines is a reflection symmetry of the decagon. Therefore, the decagon has a total of 5 reflection symmetries.
A rotational symmetry of a shape is a rotation about a fixed point that leaves the shape unchanged.
To find the number of rotational symmetries of the decagon, we can count the number of times we can rotate the decagon about its center by 36 degrees (which is the central angle of the decagon) and obtain the same shape. In this case, we can rotate the decagon about its center by 36 degrees 10 times and obtain the same shape each time.
A decagon shaped like a five-pointed star has 10 sides and 5 vertices, and it looks like this:
unitsize (1.5 cm);
pair A, B, C, D, E, F, G, H, I, J;
A = dir(108);
B = dir(72);
C = dir(36);
D = dir(0);
E = dir(-36);
F = dir(-72);
G = dir(-108);
H = dir(-144);
I = dir(-180);
J = dir(-216);
draw(A--B--C--D--E--F--G--H--I--J--cycle);
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34 pies are sold at $4.50 each.
What is the total cost of these items?
Answer:
$153
Step-by-step explanation:
Multiply the 2 numbers
where is the inequality shown? -4 to 5, 100 points for correct answer and need it urgently
9. If x+2-6x=-13 , what is the value of 2x+3?
The value of the expression 2x+3 when x = 3 is 9.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given linear equation is
x + 2 - 6x = -13
Combine like terms:
(x - 6x) + 2 = -13
-5x + 2 = -13
The additive inverse of 2 is -2.
Add -2 on both sides:
-5x + 2 -2 = -13 -2
-5x = -15
Divide both sides by -5:
-5x/-5 = -15/-5
x = 3
Putting x = 3 in the expression 2x + 3
2x + 3 = (2×3) + 3
2x + 3 =6 + 3
2x + 3 = 9
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Suppose we want to choose 2 letters, without replacement, from the 4 letters A, B, C, and D.
The number of arrangements when the order is considered is 12, Number of ways when the order is not considered is 6.
Permutaions and combinations:By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things.
The act of placing every member of a set into a certain sequence or order is known as permutation.
The combination is a method of choosing things from a group in which (unlike permutations) the order of the choices is irrelevant.
The formula for Permutations is given by
ⁿP[tex]_{r}[/tex] = (n!)/(n-r)!The formula for Combinations is given by
[tex]_{n}[/tex]C[tex]_{r}[/tex] = (n!)/r!(n - r)!Here we have
4 letters A, B, C, and D
We need to choose 2 letters from the given 4 letters
When the order of the choices is taking consideration we use the formula of Permutations
The number of ways of arrangements, ⁴P₂ = (4!)/(4-2)!
= [tex]\frac{4\times 3\times\ 2!}{2!}[/tex] = [tex]4 \times 3[/tex] = 12
When the order of the choices is not taking consideration we use the formula of Combinations
Number of ways of arrangements, ₄C₂ = (4!)/2!(4 - 2)!
= [tex]\frac{4\times 3 \times \ 2!}{2! \times 2!}[/tex] = [tex]\frac{4\times 3 }{2 \times 1 }[/tex] = [tex]2\times 3[/tex] = 6
Therefore,
The number of arrangements when the order is considered is 12, Number of ways when the order is not considered is 6.
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Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x-coordinate of point D.
The coordinate of point D and point E will be (x, y) and (-x, y), respectively.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in the m:n ratio, finding the mid-point of the line, etc.
Let the coordinate of the point D be (x, y).
Point E has a similar y-coordinate as point D. Then the ordinate of the points will be the same.
And the x-direction of point E is something contrary to the x-direction of point D. Then the coordinate of point E will be (-x, y).
The coordinate of point D and point E will be (x, y) and (-x, y), respectively.
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Find the missing length indicated.
The missing length in the given figure is 14.
What is meant by ratio?A ratio in mathematics depicts the product of two numbers. For instance, the proportion of oranges to lemons in a serving of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). In a similar vein, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8. (or 3:4). (or 4:7).
Any number of numbers, including counts of people or things, weights, lengths, and times, among other values, can be a component of a ratio. In settings, both numbers are often restricted to positive values.
A ratio's two constituent numbers can be specified as "a" and "b," or they can both be omitted.
From the given figure,
AC/BC=EC/DC
28+x/18=x/6
28+x=3x
2x=28
x=14
Therefore, the missing length in the given figure is 14.
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Iris’s checking account pays a simple interest at 2% per year. She has $175 in her account. Write a linear function to model the amount of money in her checking account at any time
The expression to model the amount of money will be 175 ^ 1.02^t.
What is the expression to model the amount?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Since Iris’s checking account pays a simple interest at 2% per year. She has $175 in her account.
The function to model the amount of money in her checking account at any time will be:
= 175 ^ (1 + 2%)^t
= 175 ^ (1 + 0.02)^t
= 175 ^ 1.02^t
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17. Geometry The figure shown is a rectangle. The green shape in the figure is a square. The blue anc white shapes are rectangles, and the area of the blue rectangle is 24 square inches.
a. Write an expression for the area of the entire figure that includes an exponent. Then find the area.
b. Find the dimensions of the entire figure.
The expression for the area that includes an exponent is 6² + (6 × 2) + 24
Area of the entire figure is 72 square inches
The dimension of the entire figure is 9 inches by 8 inches
Calculating the area of a figureFrom the question, we are to write an expression for the area of the entire figure
Area of the entire figure = Area of green shape + Area of white shape + Area of blue shape
Area of the entire figure = 6² + (6 × 2) + 24 square inches
The expression is 6² + (6 × 2) + 24
Thus,
Evaluating
Area of the entire figure = 6² + (6 × 2) + 24
Area of the entire figure = 36 + 12 + 24
Area of the entire figure = 72 square inches
b. The dimension of the entire figure
Width of the entire figure = Length of the green square + Width of the white rectangle
Width of the entire figure = 6 inches + 2 inches
Width of the entire figure = 8 inches
Then,
Length of the entire figure = Length of the white rectangle + Width of the blue rectangle
First, we will determine the width of the blue rectangle
Using the formula,
Area = l × w
Where l is the length
and w is the width
24 = (2 + 6) × w
24 = 8 × w
w = 24/8
w = 3 inches
Therefore,
Length of the entire figure = 6 inches + 3 inches
Length of the entire figure = 9 inches
Hence, the dimension is 9 inches by 8 inches
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Solve using the Square Root Property.
y^2 = 1/16
Answer:
1/4
Step-by-step explanation:
The square root of 16 is 4, so its the same with fractions.
WRITE THE EQUATION OF THE CONIC SHOWN
Answer:
x² +y² -10x -8y +21 = 0
Step-by-step explanation:
try desmos graph
Using the Weshcler IQ test, adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. b) Find the score of an individual who is at the 85th percentile.
The 85th percentile of a normal distribution is the score that is greater than or equal to 85% of the scores in the distribution. This means that the score at the 85th percentile is the same as the score that would be earned by the top 15% of individuals in the distribution.
To find the score at the 85th percentile, we can use the standard normal distribution table or use a calculator to find the z-score corresponding to the 85th percentile. The z-score is the number of standard deviations that a score is above or below the mean of the distribution.
Using a calculator or table, we find that the z-score corresponding to the 85th percentile is 1.04. Since the mean of the distribution is 100 and the standard deviation is 15, this means that the score at the 85th percentile is 100 + (1.04 * 15) = 120.4.
Therefore, the score of an individual who is at the 85th percentile on the Weshcler IQ test is 120.4.
In constructing a confidence interval for the mean, when the population standard deviation is unknown, then we use
a. normal distribution
b. binomial distribution
c. t-distribution
d. Poisson distribution
While constructing a confidence interval for the mean, when the population standard deviation is unknown, then we use normal distribution .
The error bound EBM and confidence interval are calculated using a standard normal distribution when the population standard deviation is unknown. We must determine the value of z that places an area in the centre of the standard normal distribution Z N that is equal to the confidence level (in decimal form) (0, 1).
We rarely know the population standard deviation in practise. When the sample size was huge is the , statisticians were not hindered by this. As an estimate for, they used the sample standard deviations, and they then carried out the same steps as before to compute a confidence range that produced near enough findings.
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PLSSSS HELP THX U !!!!!!
The lowest price that Mike should pay for 7 days' juice consumption is £6.16.
How to calculate the cost per item?In order to calculate the cost of one item, divide the total cost of items by the total number of items. It is also called the unit rate of that item.
The per day requirement of Mike is 2/5 liters.
Then, for 7 days the requirement is 2/5 × 7 = 14/5 liters.
The rate of juice for 2 liter and 1 liter carton are given as £4.40 and £2.60 respectively.
Then, the unit rate for both the carton is given by 4.40/2 = £2.20 and £2.60 respectively.
Since, the two liter carton has less unit rate, it can be used for 7 days consumption.
Now, the lowest price paid by mike is given as,
Unit rate of 2 liter carton × Total requirement of milk for 7 days
⇒ 2.20 × 14/5
⇒ 6.16
Hence, the lowest price paid by mike is £6.16.
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a) By completing the tables of values to help you, plot the lines y=3 x and y=x+6 on your axes.
b) Use your diagram to find the solution to the simultaneous equations y=3 x and y=x+6.
The point (3, 9) is the point which satisfies both the equation.
What is an equation?
In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =
Main body;
A)According to the given equation:
y = 3x
y = 1 , x = 3
y = 2 , x = 6
y = 3 , x = 9
for the equation ,
y = x+6
y = 6 , x = 0
y = 5 , x = -1
y = 4 , x = -2
B) as y = 3x substitute it in other equation
3x = x+ 6
2x =6
x = 3
as y = 3x
y =3*3
y = 9
Hence ,point (3, 9) is the point which satisfies both the equation.
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help wanted proportinal relationship
Answer:
guy or girl
Step-by-step explanation:
If α=.10 and β=.33, then the probability of rejecting the null when the alternative is true is ___.a. 0.10b. 0.90c. 0.33d. 0.67
The probability of rejecting the null when the alternative is true is d. 0.67
Given :
If α=.10 and β=.33, then the probability of rejecting the null when the alternative is true is .
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Null hypothesis :
A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations.
we know that ,
probability = 2 * 0.33 + 0.01
= 0.66 + 0.01
= 0.67
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A person whose eyes are 1.64 m above the floor stands 2.30 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor. What is the horizontal distance x?
When the floor is 2.30 m in front of a vertical plane mirror and the bottom edge of the mirror is 38 cm above the floor, the horizontal distance from the mirror's base to the wall is 0.6935 m.
What is trigonometry?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.
Here,
Perpendicular Length,
=Vertical Distance of eyes - Vertical distance of the bottom edge of the mirror
=1.64-0.38
=1.26 m
Angle of Reflection,
= Perpendicular Distance / Distance between the person and mirror
tan θ=1.26/2.30
tan θ=0.548
θ=tan⁻¹(0.548)
θ=28.72°
Angle of Incidence = 90 degrees - angle of reflection
=90-28.72
γ=61.28°
Angle of incidence,
=Horizontal distance to floor / height of mirror
tan 61.28°=x/0.38
x=0.38*tan 61.28°
x=0.38*1.825
x=0.6935 m
The horizontal distance to the base of the wall is 0.6935 m when the floor stands 2.30 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor.
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Luis bought some milk for his bakery. He used 2.4 gallons in one recipe, and 1/4 of the remaining miolk in another recipe. He had 3/8 of the milk left. How much milk did Luis buy?
From the values provided and basic arithmetic operations on the fractions, The answer is 4.8 gallons.
What are fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
milk brought = x
used in one recipe = 2.4
1/4 th of remaining milk = (x-2.4)/4
remaining at end = 3/8 of x
final equation,
x-(2.4+(x-2.4)/4)=3x/8
5x/8=2.4+x/4-3/5
5x/8=1.8+x/4
3x/8=1.8
x=4.8 gallons
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Which graph represents the function f(x) = 2x-1/ x-1
To determine which graph represents the function [tex]$f(x)=\frac{2 x-1}{x-1}$[/tex]make following steps:
What is function?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x^2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Four main categories may be used to classify different sorts of functions. dependent upon element Function is defined as one to one, many to one, onto, one to one and into function.
1. The vertical asymptote is x=1.
2. Simplify the function[tex]f(x)=\frac{2 x-1}{x-1}=\frac{2 x-1-1+1}{x-1}=\frac{2(x-1)+1}{x-1}=2+\frac{1}{x-1}$[/tex].
Then the horizontal asymptote is y=2.
Only option C contains graph with such asymptotes.
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please help me thank you so much
Answer: 2* (2w + w) = 60
Step-by-step explanation: I believe this is correct because to find the perimeter, we need to add both length and width, so this answer is the only one that expresses 2w + w being multiplied by 2 to get 60. I hope this helped.
The graph shows the coordinates of triangle ABC. What are the coordinates of B' after a
reflection over the y-axis.
Answer:
(-4,5)
Step-by-step explanation: