8. The diagram shows the triangle PQR. In the diagram, all the angles are in degrees. RP = RQ Find the value of y. Show clear algebraic working. P= 2x + 10, R=y, Q= X + 15
Answers
The value of y in the given isosceles triangle is 140°.
What is isosceles triangle?A triangle with two equal edges is said to be isosceles. Also equal are the two angles that face the two identical sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
If the sides AB and AC of a triangle ABC are equivalent, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is also congruent," states the theorem that explains the isosceles triangle.
What is an angle?An angle is a shape created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two beams are in the plane where the rays are located. The meeting of two surfaces also creates angles.
In the given question,
∠P=∠Q
2x+10=x+15
x=5
Therefore,
∠P=2(5)+10=20°
∠Q=5+15= 20°
∠P+∠Q+∠R= 180°
20+20+∠R= 180°
∠R= 140°
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Related Questions
Find the center and radius of the circle whose equation is x^2+y^2+4y=32
Answers
Answer:
center: (0, -2)
radius: 6
Step-by-step explanation:
You have to "complete the square" this allows you to fold up the expressions and put the equation in a standard kinda of format where you can pick the center and radius right out of the equation.
see image.
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a 3
Answers
Answer:
the answer is 12/13 simplified
Step-by-step explanation:
simplified
Solve using the correct order of
operations.
P
E
MD
AS
15-(4-3) 2= [?]
Enter
Help
Answers
Here using the correct order of operations that is PEMDAS, we get the value to be 13.
Define PEMDAS?PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.
The letters stand for:
P stands for parentheses.
Exponents are shown as E.
D stands for division.
The letter M stands for multiplication.
A stand for addition.
S stands for subtraction.
Now in the given question,
15 - (4-3)2
First the parentheses
15 - (1)2
Next is exponents.
15 - 2
At last, after subtracting, we get:
13
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what is true and what is not for this right triangle need help
Answers
Step-by-step explanation:
For RIGHT triangles, using S-O-H-C-A-H-T-O-A
A sinA= cosB yes 12/13 = 12/13
B. sinA=tanB no 12 /13 not equal to 5/12
C. sinB= tanA no 5/13 not equal to 12/5
D. sinB= cosB no 5/13 not equal to 12/13
A) sinA= cοsB statement is true. Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A.
What is a triangle?A triangle is a twο-dimensiοnal geοmetric shape that cοnsists οf three straight line segments, called sides, that cοnnect three nοn-cοllinear pοints, called vertices.
Based οn the given image, the fοllοwing statements are true:
1. The triangle is a right triangle, which means that οne οf the angles is a right angle (90 degrees).
2. The side οppοsite the right angle is called the hypοtenuse, which is the lοngest side οf the triangle. In this case, it is the side that is labeled "c".
3. The οther twο sides οf the triangle are called legs. In this case, they are labelled "a" and "b".
4. The Pythagοrean theοrem applies tο this triangle, which states that the sum οf the squares οf the lengths οf the legs is equal tο the square οf the length οf the hypοtenuse. In οther wοrds, [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].
Fοr RIGHT triangles, using S-O-H-C-A-H-T-O-A
A sinA= cοsB yes 12/13 = 12/13
B. sinA=tanB nο 12 /13 nοt equal tο 5/12
C. sinB= tanA nο 5/13 nοt equal tο 12/5
D. sinB= cοsB nο 5/13 nοt equal tο 12/13.
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Complete Question:
In Δ ABC , angle C is right Angle
Which Statement must be True?
A sinA= cosB
B. sinA=tanB
C. sinB= tanA
D. sinB= cosB
Synthetic Division to Find Zeros
if f(x)=x^3−3x^2+16x+20 and x+1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answers
Answer:
Step-by-step explanation:
Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.
We set up synthetic division as follows:
-1 | 1 -3 16 20
| -1 4 -20
|_____________
1 -4 20 0
The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:
x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))
= (4 ± sqrt(-64)) / 2
= 2 ± 2i√2
Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.
The weight of a miniature Tootsie roll is normally distributed with a mean of 3.30 grams and standard deviation of .13 gram
Answers
We can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams for standard deviation of 0.13 gram.
What is a normal distribution?A normal distribution is a symmetric, bell-shaped continuous probability distribution that is defined by its mean and standard deviation. The majority of the data in a normal distribution is located close to the mean, and the number of data points decreases as you deviate from the mean in either direction. Because many real-world events, like human height or test scores, have a tendency to follow a normal distribution, the normal distribution is frequently utilised in statistics. A helpful technique for determining the range of values within a normal distribution based on the mean and standard deviation is the empirical rule, commonly known as the 68-95-99.7 rule.
Given that, the mean of 3.30 grams and standard deviation of 0.13 gram.
Using the empirical formula the range that falls in 95% is associated to two standard deviations.
Mean + 2 standard deviations = 3.30 + 2(0.13) = 3.56 grams
Mean - 2 standard deviations = 3.30 - 2(0.13) = 3.04 grams
Hence, we can estimate that the middle 95% of all miniature Tootsie rolls will fall within the range of 3.04 grams to 3.56 grams.
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please find the midpoint of the following line and arc using straightedge-compass-construction method
Answers
The midpoint of a line or arc can be found using straight edge-compass-construction method by drawing two perpendicular bisectors. The intersection of these bisectors is the midpoint.
To find the midpoint of a line segment, first draw a straight line passing through both endpoints of the segment using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the line segment. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the line segment. The intersection of these bisectors is the midpoint of the line segment.
To find the midpoint of an arc, first draw a chord that intersects the arc at two points using a straight edge. Then, using a compass, draw two circles with the same radius centered at each endpoint of the chord. The circles should intersect at two points. Draw straight lines connecting these two points to form two perpendicular bisectors of the chord. The intersection of these bisectors is the center of the circle that the arc belongs to. Draw a line from the center of the circle to the midpoint of the chord. This line will intersect the arc at its midpoint.
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--The question is incomplete, answering to the question below--
"find the midpoint of a line and arc using straight edge-compass-construction method"
Do X4 and 15+ X have the same value when X is 5
Answers
Find the surface area of the figure on the right.
Answers
The fig's right side of total surface = 42yds.
What is surface area?
A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
According to our question-
(17+17+8)yds
42yds
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What does replacement value in math? Say if you have to find a replacement value for the variable X, what does that mean?
Answers
A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.
What is an expression?An expression is a combination of numbers, variables, and/or operators that represents a mathematical relationship or calculation. An expression can be as simple as a single number or variable, or it can be more complex and involve multiple operations and variables.
What is a variable?A variable is a symbol or letter that represents a quantity or value that can change or vary in different contexts.
In the given question,
A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.
For example, suppose you have the equation 2x + 3 = 7, and you want to solve for x.
To do so, you can use a replacement value.
You can subtract 3 from both sides of the equation to isolate the term with x, which gives you:
2x = 4
Now, you can divide both sides of the equation by 2 to solve for x:
x = 2
In this case, the replacement value was the number 2, which was substituted for the variable x in the equation in order to solve for x.
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The area of a trapezium is 156cm2, the parallel sides are 17cm and 35cm respectively. What is the height of the trapezium
Answers
Answer:
6 cm
Step-by-step explanation:
You want the height of a trapezium with bases 17 cm, 35 cm and area 156 cm².
Area formulaThe formula for the are of a trapezium is ...
A = 1/2(b1 +b2)h
Filling in the given values, we have ...
156 = 1/2(17 +35)h = 26h
6 = h . . . . . . . . . . divide by 26
The height of the trapezium is 6 cm.
Answer:
6cm
Step-by-step explanation:
To find:-
The height of the trapezium.Answer:-
We are here given that the area of the trapezium is 156cm² and two of the parallel sides are 17cm and 35cm .We are interested in finding out the height of the trapezium.
The area of the trapezium is given by the formula,
[tex]:\implies \sf Area =\dfrac{1}{2}\times (s_1+s_1)\times h \\[/tex]
where s1 and s2 are the || sides of the trapezium and h is the height of the trapezium.
Now on substituting the respective values in the given formula, we have;
[tex]:\implies \sf 156cm^2 =\dfrac{1}{2} (17cm+35cm)\times h \\[/tex]
[tex]:\implies \sf 156cm^2(2) = 52cm (h) \\[/tex]
[tex]:\implies \sf h =\dfrac{156(2)}{52} cm\\[/tex]
[tex]:\implies \sf \pink{ height = 6 cm }\\[/tex]
Hence the height of the trapezium is 6cm .
At a certain instant, the base of a triangle is 5 inches and is increasing at the rate of 1 inch per minute. At the same instant, the height is 10 inches and is decreasing at the rate of 2.5 inches per minute. Is the area of the triangle increasing or decreasing? Justify your answer.
Answers
Using differentiation, the area of the triangle is decreasing at the given time.
Is the area of the triangle increasing or decreasing?The formula for the area of a triangle is:
A = (1/2)bh
where b is the base and h is the height.
Differentiating both sides of the equation with respect to time t, we get:
[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]
Substituting the given values, we get:
[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]
Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.
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Determine the following standard normal (z) curve areas. (Round all answers to four decimal places.)
(a) The area under the z curve to the left of 1.73
(b) The area under the z curve to the left of
−0.69
(c) The area under the z curve to the right of 1.3
(d) The area under the z curve to the right of
−2.82
(e) The area under the z curve between −2.22 and 0.52
(f) The area under the z curve between
−1
and 1
(g) The area under the z curve between
−4
and 4
Answers
(a) The area under the standard normal curve to the left of 1.73 is 0.9582.
(b) The area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area under the standard normal curve to the right of 1.3 is 0.0968.
(d) The area under the standard normal curve to the right of -2.82 is 0.9974.
(e) The area under the standard normal curve between -2.22 and 0.52 is 0.6851.
(f) The area under the standard normal curve between -1 and 1 is 0.6826.
(g) The area under the standard normal curve between -4 and 4 is 0.9998.
(a) Using a standard normal table, the area under the standard normal curve to the left of 1.73 is 0.9582.
(b) Similarly, the area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area to the right of 1.3 is the same as the area to the left of -1.3. Using a standard normal table, this area is 0.0968.
(d) The area to the right of -2.82 is the same as the area to the left of 2.82. Using a standard normal table, this area is 0.9974.
(e) To find the area under the standard normal curve between -2.22 and 0.52, we need to find the area to the left of 0.52 and subtract the area to the left of -2.22. Using a standard normal table, we find that the area to the left of 0.52 is 0.6990 and the area to the left of -2.22 is 0.0139. Therefore, the area between -2.22 and 0.52 is 0.6990 - 0.0139 = 0.6851.
(f) To find the area under the standard normal curve between -1 and 1, we need to find the area to the left of 1 and subtract the area to the left of -1. Using a standard normal table, we find that the area to the left of 1 is 0.8413 and the area to the left of -1 is 0.1587. Therefore, the area between -1 and 1 is 0.8413 - 0.1587 = 0.6826.
(g) The area under the standard normal curve between -4 and 4 is the same as the area to the left of 4 minus the area to the left of -4. Using a standard normal table, we find that the area to the left of 4 is 0.9999 and the area to the left of -4 is 0.0001. Therefore, the area between -4 and 4 is 0.9999 - 0.0001 = 0.9998.
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In a survey of 124 pet owners, 44 said they own a dog, and 58 said they own a cat. 14 said they own both a dog and a cat. How many owned neither a cat nor a dog?
Answers
Step-by-step explanation:
See Venn diagram below
If a + b = 3 and ab = 2, find the value of a² + b²
Answers
Answer:
Through observation, a=2, b=1 or vice versa .
Step-by-step explanation:
If a=2 and b=1
a² +b²=?
2² +1² =4+1=5
a²+b²=5
The function f(x) is represented by this table of values.
x f(x)
-5 35
-4 24
-3 15
-28
-1
3
0
0
1 -1
Match the average rates of change of fx) to the corresponding intervals.
-8
-7
(-5, -1]
(-4,-1]
[-3, 1]
(2, 1)
HELPPP ASAP
Answers
Answer:
-8: (-4, -3]
-7: (-3, -1]
(-5, -1]: (-5, -1]
(-4, -1]: (-4, -1]
[-3, 1]: [-3, 1]
(2, 1): (1, 2]
BRAINEST IF CORRECT! 25 POINTS.
What transformation of Figure 1 results in Figure 2?
Select from the drop-down menu to correctly complete the statement.
A ______ of Figure 1 results in Figure 2.
Answers
Answer:
its reflection
Step-by-step explanation:
a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Answer:
It is Reflection. Check if it is in the list.
can you find c and b?
c=?
b=?
Answers
The value of the constant c that makes the following function are c = 0.
What is constant ?Constant is a term used to describe a value that remains unchanged or fixed throughout a program or process. It can be a numeric value, a character value, a string, or a Boolean (true/false) value. Common examples of constants include physical constants, mathematical constants, and programming-language keywords.A constant is a value that does not change, regardless of the conditions or context in which it is used. Common examples of constants include mathematical values such as pi (3.14159), physical constants such as the speed of light (299,792,458 m/s), and other constants such as the universal gravitational constant (6.67408 × 10−11 m3 kg−1 s−2).
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Therefore, c must equal 0 in order for the two sides of the function to be equal. and The one with the greater absolute value is b = 10.
What is function?A function is a block of code that performs a specific task. It is a subprogram or a set of instructions that can be used multiple times in a program.
27. For the function to be continuous at x = 7, the limit of the function as x approaches 7 from the left must equal the limit of the function as x approaches 7 from the right.
This means that the value of y as x approaches 7 must be the same on both the left and right sides of the point.
Since the left side of the function is y = c*y + 3, the right side of the function must also be equal to y = c*y + 3.
Therefore, c must equal 0 in order for the two sides of the function to be equal.
28. In order for the function to be continuous at x = 5, the value of y at x = 5 must be the same on both the left and right sides of the point.
Since the left side of the function is y = b - 2x, the right side of the function must also be equal to y = b - 2x.
Therefore, b must equal 10 in order for the two sides of the function to be equal.
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Complete Question:
PLEASE HELP !!!! HELP!!label each equation is proportionality or non proportional Help
y=9/x
y=x-12
h=3d
f=1/3e
Answers
Answer:
y=9/x => proportional
y = x - 12 ==> non-proportional
h = 3d ==> proportional
f = 1/3 e = proportional
Step-by-step explanation:
A proportional equation is of the general form
y = kx (directly proportional) or
y = k/x (inversely proportional)
k is known as the constant of proportionality
y = 9/x ==> k = 9 proportional
y = x - 12 cannot be expressed as y = kx or y = k/x
h = 3d ==> k = 3 proportional
f = 1/3 e ==> k = 1/3 proportional
You are crossing two pea plants. One is heterozygous for yellow. The second pea plant is homozygous for green. Use "G/g" as the letter to represent the gene for this problem.
Answers
The result of the cross breeding between the heterozygous and homozygous pea plant is the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
What is the result of crossbreeding?In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).
When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).
The possible combinations of alleles that the offspring can inherit from their parents are:
Gg x gg
Gametes from the Gg plant: G, gGametes from the gg plant: g, gPossible genotypes of offspring: Gg, gg (50% chance for each)Possible phenotypes of offspring: yellow (Gg) or green (gg) in a 1:1 ratioTherefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
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can anyone help with this triangle question
Answers
Step-by-step explanation:
Set it up as a ratio:
14 is to (14 +6) as 21 is to ?
14/20 = 21/?
? = 21 * 20 / 14 = 30 units
ne al Compute the derivative of the given function. TE f(x) = - 5x^pi+6.1x^5.1+pi^5.1
Answers
The derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
In this case, the function f(x) is a polynomial, which means it is a combination of terms of the form [tex]ax^b[/tex], where a and b are constants. The derivative of f(x) can be calculated by taking the derivative of each term in the function and then combining them together.
The derivative of a term [tex]ax^b[/tex] is [tex]abx^(b-1)[/tex]. For the first term of f(x),[tex]-5x^pi[/tex], the derivative is [tex]-5pi x^(pi-1)[/tex]. For the second term, [tex]6.1x^5.1[/tex] the derivative is[tex]6.1 * 5.1x^(5.1-1)[/tex]. For the third term, [tex]pi^5.1[/tex], the derivative is [tex]5.1pi^(5.1-1)[/tex].
Combining these terms together, the derivative of f(x) is
[tex]f'(x) = -5pi x^(pi-1) + 6.1 * 5.1x^(5.1-1) + 5.1pi^(5.1-1)[/tex].
This answer is the derivative of the given function. This is how the function changes as its input changes.
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The derivative of f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex] which can be calculated with the power rule.
What is derivative?The derivative of a function is a measure of how that function changes as its input changes. Derivatives are also used in calculus to find the area under a curve, or to solve differential equations.
The derivative of the given function f(x) = [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] can be calculated with the power rule, which states that the derivative of xⁿ is nx⁽ⁿ⁻¹⁾
To calculate the derivative of the given function, we begin by applying the power rule to each term.
The first term is [tex]-5^{\pi }[/tex] which has a derivative of [tex]-5\pi x^{\pi -1}[/tex].
The second term is [tex]6.1x^{5.1}[/tex] which has a derivative of [tex]6.1*5.1x^{5.1-1}[/tex].
The third term is [tex]\pi^{5.1}[/tex], which has a derivative of 5.1[tex]\pi^{5.1-1}[/tex].
Therefore, the derivative of the given function
f(x)= [tex]-5x^{\pi}+6.1x^{5.1}+\pi^{5.1}[/tex] is [tex]-5\pi x^{\pi -1}[/tex]+ [tex]6.1*5.1x^{5.1-1}[/tex] +5.1[tex]\pi^{5.1-1}[/tex].
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Question:
Compute the derivative of the given function.
f(x) = - [tex]5x^{\pi }[/tex]+[tex]6.1x^{5.1}[/tex]+[tex]\pi^{5.1}[/tex]
Suppose that, for budget planning purposes, the city in Exercise 24 needs a better estimate of the mean daily income from parking fees.
a) Someone suggests that the city use its data to create a confidence interval instead of the interval first created. How would this interval be better for the city? (You need not actually create the new interval.)
b) How would the interval be worse for the planners?
c) How could they achieve an interval estimate that would better serve their planning needs?
d) How many days' worth of data should they collect to have confidence of estimating the true mean to within
Answers
a) As per the given budget, the amount of interval that would be better for the city is 95% confidence interval.
b) The interval that be worse for the planners is depends on sample size
c) They achieve an interval estimate that would better serve their planning needs is depends on margin of error
d) The number of days worth of data should they collect to have confidence of estimating the true mean to 30 days
To obtain a better estimate, the city can create a confidence interval, which is a range of values that is likely to contain the true population mean with a certain degree of confidence.
However, there are also some disadvantages to using a confidence interval. The interval estimate may be wider than a point estimate, which means that the budget planners may have to allocate a larger budget to account for the uncertainty in the estimate.
To achieve a better interval estimate, the city could increase the sample size or reduce the variability of the data. Increasing the sample size reduces the margin of error and increases the precision of the estimate.
Finally, to determine how many days' worth of data the city should collect to estimate the true mean with a certain degree of confidence, the city would need to consider the desired level of precision, the variability of the data, and the desired level of confidence.
Typically, a larger sample size will provide a more accurate estimate, but this also depends on the variability of the data. In general, a sample size of at least 30 is recommended for a reasonably accurate estimate.
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if you could please help i am having issues
Answers
Since the p-value (0.0803) exceeds the significance threshold (0.05), the null hypothesis cannot be ruled out.
what is mean ?The mean in mathematics is a measurement of a collection of numerical data's central tendency. It is determined by adding up all of the values in the set and dividing the result by the total number of values. This value is frequently referred to as the average value. The mean (or mathematical mean) is calculated as follows: (Sum of Values) / Mean (number of values)
given
The null hypothesis states that the mean number of units generated during the day and night shifts is the same. The contrary hypothesis (Ha) states that more units are created on average on the night shift than on the day shift.
"day" + "night"
Bravo! Night precedes day.
b. The following method can be used to calculate the test statistic:
t = sqrt(1/n night + 1/n day) * sqrt(x night - x day)
where s p is the pooled standard deviation and x night and x day are the sample averages, n night and n day are the sample sizes, and s p is represented by:
Sqrt(((n night - 1)*s night2 + (n day - 1)*s day2) / (n night + n day - 2)) yields the value s p.
S p is equal to sqrt(((74 - 1)*35 + (68 - 1)*28) / (74 + 68 - 2)), which equals 31.88.
t = (358 - 352) / (31.88 * sqrt(1/74 + 1/68)) = 1.19
1.19 is the test result.
the p-value is 0.0803 as a result (rounded to 4 decimal places).
Since the p-value (0.0803) exceeds the significance threshold (0.05), the null hypothesis cannot be ruled out.
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The complete question is :- Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. The mean number of units produced by a sample of 68 day-shift workers was 352. The mean number of units produced by a sample of 74 night-shift workers was 358. Assume the population standard deviation of the number of units produced is 28 on the day shift and 35 on the night shift.
Using the 0.05 significance level, is the number of units produced on the night shift larger?
a. State the null and alternate hypotheses.
O : Day/Night: H:
Day Night
b. Compute the test statistic. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
c. Compute the p-value. (Round your answer to 4 decimal places.) p-value
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment..
Answers
The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
Explain about the sample space of an event?A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.
When this happens, we want to give each event—like rolling a two—a number that represents the likelihood of the occurrence and describes how probable it is that it will occur. Similar to this, we would like to give any event or group of outcomes—say rolling an even number—a probability that reflects how possible it is that the occurrence will take place if the experiment is carried out.Martin features a spinner with four compartments marked A, B, C, and D.
To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.
Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.
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Alexander and Rhiannon left school at the same time. Alexander travelled 14 km home at an average speed of 20 km/h. Rhiannon travelled 10 km home at an average speed of 24 km/h. a) Who arrived home earlier? b) How much earlier did this person arrive at home? Give your answer to the nearest minute.
Answers
Rhiannon arrived home approximately 17 minutes earlier than Alexander.
What is the average?This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
According to the given information:To solve this problem, we can use the formula:
time = distance / speed
a) The time it took Alexander to get home is:
time_Alexander = 14 km / 20 km/h = 0.7 hours
The time it took Rhiannon to get home is:
time_Rhiannon = 10 km / 24 km/h = 0.41667 hours
Since Rhiannon's time is smaller than Alexander's, Rhiannon arrived home earlier.
b) The time difference between their arrivals is:
time_difference = time_Alexander - time_Rhiannon = 0.7 hours - 0.41667 hours = 0.28333 hours
To convert this to minutes, we can multiply by 60:
time_difference_in_minutes = 0.28333 hours x 60 minutes/hour ≈ 17 minutes
Therefore, Rhiannon arrived home approximately 17 minutes earlier than Alexander.
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The lunch special at Maria's Restaurant is a sandwich and a drink. There are 2 sandwiches and 5 drinks to choose from. How many lunch specials are possible?
Answers
Answer:
the question is incomplete, so I looked for similar questions:
There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.
the answer = 3 x 4 x 2 = 24 possible combinations
Explanation:
for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich
since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24
If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.
For this question's answer, there are 2 x 5 = 10 lunch specials are possible.
The number of lunch specials possible are 10.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
We are given that;
Number of sandwiches=2
Number of drinks=5
Now,
To find the total number of lunch specials, we need to multiply the number of choices for sandwiches by the number of choices for drinks.
Number of sandwich choices = 2
Number of drink choices = 5
Total number of lunch specials = 2 x 5 = 10
Therefore, by combinations and permutations there are 10 possible lunch specials.
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if A is 20% more than B, by what percent is B less than A?
Answers
Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:
A = B + 0.2B
Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:
A = 1.2B
Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:
(B lebih kecil dari A) / A x 100%
Substitusikan nilai A = 1.2B dan kita dapatkan:
(B lebih kecil dari 1.2B) / 1.2B x 100%
Maka:
0.2B / 1.2B x 100%
= 0.1667 x 100%
= 16.67%
Jadi, B adalah 16.67% lebih kecil dari A.
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 9 feet. Container B has a diameter of 8 feet and a height of 20 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
Answers
Step-by-step explanation:
the volume of container B is Travers from A to B.
so, the volume of the empty space in A is exactly the volume of container B.
the volume of a cylinder is
base area × height = pi×r² × height.
the reside is as always half of the diameter.
r = 8/2 = 4 ft
the volume of the empty space in A = the volume of container B =
= pi×4² × 20 = pi×16 × 20 = 320pi = 1,005.309649... ≈
≈ 1,005.3 ft³
HELP PLEASEEE 30 POINTS!!
Answers
Answer:
m<1 = 63° (Exterior alternating Angles)
m<2 = 62°
m<3 = 118°
Step-by-step explanation:
[tex]{ \tt{m \angle 2 + 63 \degree + 55 \degree = 180 \degree}} \\ { \sf{(exterior \: corresponding \: angles)}} \\ { \tt{m \angle 2 = 180 - (63 + 55)}} \\ { \tt{ \underline{ \: m \angle 2 = 62 \degree \: }}}[/tex]
[tex]{ \tt{m \angle 3 = m \angle 1 + 55 \degree}} \\ { \tt{m \angle 3 = 63 + 55}} \\ { \tt{ \underline{ \: m \angle 3 = 118 \degree \: }}}[/tex]
